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I'm developing a hierarchical model with 5 depen, 1 indepen, and 2 mediating elemetns (n=180).
Thru EFA, only 4 factors survived before tesed in CFA with great model fit. However,every item failed the 0.5 of EVA and CR. To continue would be meaningless so I'm wondering is there anything else I can do?
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Hi,
if your AVE and CR are "terrible" that means that the loadings must be low. This happens due to two reasons
1) The model is correctly specified but the measurement error is high
2) The model is misspecified. In my experience, low loadings are mostly due to #2
What was the model's chi-square test? If if it fits, the sample size is rather low implying a low power to reject the model.
This is no disaster.
1) Apply the SWAIN correction to the model testing
2) Respecify the model which will probably mean to increase the number of latent variables or its complexity
Study 2 in this paper provides an illustration of model diagnostics and respec:
Rosman, T., Kerwer, M., Steinmetz, H., Chasiotis, A., Wedderhoff, O., Betsch, C., & Bosnjak, M. (2021). Will COVID‐19‐related economic worries superimpose health worries, reducing nonpharmaceutical intervention acceptance in Germany? A prospective pre‐registered study. International Journal of Psychology. https://doi.org/doi.org/10.1002/ijop.12753
If you respec, note the limitations (data dredging) and be transparent. Whether this will decrease your likelihood to get the paper published is different story ;)
Best,
Holger
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Previously I calculated the bunch of above 50 items by some extraordinary way and got 3 scales and now recalculating them as it should be.
Previously I used Statistica 12.0 and AMOS 23.0. Now for EFA I’m using Factor 12.03.01 64 bits (https://psico.fcep.urv.cat/utilitats/factor/Download.html).
So, concerning the number of factors:
- Hull recommends me 1 factor,
- MAP – 3 factors,
- Parallel analysis – 5 factors.
As I know from my previous exploration of these items, 3 factors for the first steps are bad interpretable and very noisy. If we take 5 factors, they are quite understandable but by step by step removing weak items will be got the structure of 3 or maybe 4 factors (scales).
So, concerning the item selection.
Factor 12.03 gives me a bunch of opportunity. But which of them should be consider as statistical criteria for selecting items and which of them are common ‘decision rules’ for selecting items and how one can prove this decision rules?
Factor 12.03. provides measurement of sample adequacy, MSA (Lorenzo-Seva & Ferrando, 2021) everywhere as such criteria. I like and appreciate this opportunity but at initially steps of selecting items it brings some risks for washing out scales with low quantity of items and for washing out some unique questions with low communalities.
I would like to use D, communality-standardized Pratt’s measure (Wu & Zumbo, 2017), as a criterion for items selection at very first steps because in considering (a) the unique contribution of a factor to an item’s observed variation (i.e. Pratt’ss measure) and (b) uniqueness of questions.
For example, I have an item V58. Factor 12.03 suggests that I remove it because of prefactor solution.
Items Normed 95% Confidence The Pool
MSA interval
----- ------------------------- --------
58 0.661 (0.493 -- 0.726) Might not work - Revise
----- ------------------------- --------
I would lice to see how V58 should be bad
So what I have found by further Factor 12.03 using.
Variable Mean Confidence Interval Variance Skewness Kurtosis
(95%) (Zero centered)
s_12_58 3.300 ( 3.21 3.39) 0.885 -0.061 0.008
Good
Variable 58
Value Freq
|
1 24 | ***
2 78 | *********
3 320 | ****************************************
4 174 | *********************
5 77 | *********
+-----------+---------+---------+-----------+
0 80.0 160.0 240.0 320.0
Almost excellent
ROTATED LOADING MATRIX
Variable F 1 F 2 F 3 F 4 F 5
s_12_58 0.160 0.257 0.002 0.065 -0.008
The loadings are low. Maybe one should exclude V58, because loadings are less than |0.300|. It is one of decision rules (but I don’t know how I can prove it). Let’s see other V58 characteristics.
UNROTATED LOADING MATRIX
Variable F 1 F 2 F 3 F 4 F 5 Communality
s_12_58 0.076 -0.233 -0.147 -0.016 -0.038 0.083
But because of low communality V58 should be unique.
It means that afterwards
COMMUNALITY-STANDARDIZED PRATT'S MEASURES
Variable F 1 F 2 F 3 F 4 F 5
s_12_58 0.161 0.771 0.000 0.064 0.004
These communality-standardized Pratt's measures for V58 look optimistic, so V58 shouldn’t be removed at least during these first steps.
And I should assess some residuals.
Largest Negative Standardized Residuals
Residual for Var 39 and Var 6 -2.95
Residual for Var 58 and Var 6 -2.70
Largest Positive Standardized Residuals
Residual for Var 8 and Var 6 2.65
Residual for Var 42 and Var 6 2.58
Residual for Var 52 and Var 23 2.96
Residual for Var 54 and Var 6 3.23
Residual for Var 58 and Var 28 2.63
Residual for Var 58 and Var 52 2.61
And for my sorrow bunch of Indices for detecting correlated residuals (doublets) should not work in Factor 12.03 because program calculate these indices with all excluded variables (((.
So, concerning items selection the questions are:
- If one so interested in communality-standardized Pratt's measures why can he formulate or prove the decision rule for it. Is it decision rule or statistical criterion?
- When and why should be used MSA, if it probably depends of ‘noise’ items and proportions of quantity of items in scales?
- How could one prove the cutoff of 0.300 for loadings?
- Which are decision rules for standardized residuals?
Thank you very much I’ll be happy every advice in this sphere.
Lorenzo-Seva, U., & Ferrando, P. J. (2021). MSA: The forgotten index for identifying inappropriate items before computing exploratory item factor analysis. Methodology, 17(4), Article 4. https://doi.org/10.5964/meth.7185
Wu, A., & Zumbo, B. (2017). Using Pratt’s Importance Measures in Confirmatory Factor Analyses. Journal of Modern Applied Statistical Methods, 16(2), 81–98. https://doi.org/10.22237/jmasm/1509494700
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There are several statistical criteria that can be used to select items for inclusion in an exploratory factor analysis (EFA). Some common criteria include:
  1. Factor loadings: Factor loadings are the correlation between an item and the factor it is loading on. Items with high factor loadings (typically above .3 or .4) are considered good indicators of the factor they are loading on and are typically retained in the analysis.
  2. Communalities: Communalities are the proportion of variance in an item that is explained by the factors in the analysis. Items with high communalities (typically above .6) are considered good indicators of the factors and are typically retained in the analysis.
  3. Eigenvalues: Eigenvalues are a measure of the amount of variance in the data explained by each factor. Factors with high eigenvalues are typically retained in the analysis, as they explain a significant amount of the variance in the data.
  4. Parallel analysis: Parallel analysis is a technique that compares the eigenvalues obtained in the data with those obtained from a simulated dataset in order to determine the number of factors to retain.
  5. scree plot: A scree plot is a graph that plots the eigenvalues of the factors on the y-axis and the factor number on the x-axis, it helps to identify the point at which the eigenvalues level off and stop decreasing, this point is called the "elbow" of the plot and it is typically used to determine the number of factors to retain in the analysis.
It is important to note that these criteria are not mutually exclusive, and multiple criteria may be used in combination to make the final decision about which items to retain in the analysis. Additionally, the choice of criteria may depend on the research question and the specific goals of the analysis.
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Dear all, I am conducting research on the impact of blockchain traceability for charitable donations on donation intentions. One scale/factor measures “likelihood to donate” consisting of 3 items (dependent variable). Another ”trust” factor, consisting of 4 items (potential mediator). Furthermore, a “perception of quality” consisting of 2 items (control). And a scale “prior blockchain knowledge” consisting of 4 items (control). My question is: since all these scales are taken from prior research, is CFA sufficient? Or, since the factors are from different studies (and thus have never been used together in one survey/model) should I start out with an EFA?
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As Prof. Geiser commented, for the four variables, given that they are quite distinctive from each other in terms of the content, and have been developed in the previous studies, CFA is sufficient.
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I am developing a questionnaire for social science. The preliminary questionnaire has 35 items with 6 domains. However, one of the domains was optional ( 5 items), where only those who had been involved in an accident before needed to answer that questions. Unfortunately, my answer option for answering the questionnaire did not include not applicable.
When I run the EFA, parallel analysis suggests 5 factors. But this optional domain loads closely with another item with different instructions/ other domains.
So my question is, can I remove this one domain ( 5 items) from the EFA analysis and run the remaining 30 items for EFA. Then, re-include this optional domain when I run for CFA. Can I use expert judgment /based on the importance of that optional domain to the questionnaire to retain it as it is?
( I try to rerun the 35 items and 6 domain/factor ( including the optional domain) using CFA, and the result indicated good convergent and discriminant validity)
I wonder if this method is permissible or how I should go about it? Thanks
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Ms Khaireena When constructing a questionnaire, several dimensions or scales can be used for exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). However, it is critical to evaluate the consequences of such a decision and to be open about the technique in your study report.
When utilizing EFA, it appears that the optional domain does not mesh well with the other questions in the questionnaire in your scenario. Removing it from the EFA analysis and then re-adding it in the CFA analysis might be a viable strategy, as long as the optional domain is still relevant to the overarching research topic and you have a strong rationale for including it in the CFA.
It's also worth noting that when you use CFA, you're testing a specific model, and this optional domain must load exactly as you described in your model. If it does not fit well in the model, it may impair the validity of your results, therefore keep that in mind while selecting whether to include or omit this domain.
Expert judgment can be used to support your decision to keep the optional domain, but it's also important to use other validation methods, such as cross-validating your results with other methods of analysis and performing sensitivity analysis to see how the results change with different sample sizes or model specifications.
To summarize, it is critical to be honest about your research methodologies and to examine the ramifications of deleting an optional domain from the EFA analysis while including it in the CFA analysis. Cross-validating your data with different techniques of analysis is also advised, as is consulting with an expert in SEM or a statistician to have a better understanding of the results.
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I am conducting a research which involves scale development for emotional experiences with Wanghong (Internet-famous) restaurant dining consumption. With reference to the steps in prior literature, I have already done interview and expert review on the measurement scales. It is interesting to see that the emotional experiences may be categorized into three stages, pre-, during, and post-dining experience. I have conducted the first study, with the objective to purify the scale. I have done one analysis on all the measurement items using EFA without the consideration of three stages, and four factors emerged. In order to reflect the finding that emotional experiences are different in the three stages, I think three EFAs should be conducted? It seems to me that the first way is more methodological correct, while the second way is more theoretically or conceptually correct. Would appreciate if anyone may give me some advices on this! Thanks a lot!
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Yes , I do .
With our appreciation to your scientific efforts doctor ,
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Dear Research Scholars, you are doing well!
I am a Ph.D. scholar in Education. Now I am working on my thesis. kindly guide me that when to perform the EFA whether it use on pilot studying data or actual research data.
Regards
Muhammad Nadeem
Ph.D. In Education , faculty of Education,
University of Sindh, Jamshoro
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When you need to hypothesise a connection between variables, exploratory factor analysis is the method to apply.
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I am conducting an exploratory factor analysis and to determine the number of factors I used a paired analysis.
How can I generate the number of factors correctly in stata? Or other tool?
When using parallel analysis in stata, for example, if you proceed with Principal Axis Factoring all my Eigenvalues from the Parallel Analysis using a Principal Axis Factoring lower than 1. (Suggests in this case to retain all factors)
when out of curiosity, I use principal component factors, or even principal component analysis (I know this is not EFA), it suggests retaining 3 factors (which satisfies me)
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Hi there,
the most basic question is whether a common factor model (which underlies EFA) is reasonable. Are your indicators of a kind that makes the assumption reasonalbe that they were caused by one or several underlying common causes? How does the correlation matrix looks like?
If a PCA is better than this suggests that the former assumption is unreasonable. This is fine but keep in mind that a PC is a simple composite of the indicator without any surplus meaning.
HTH
Holger
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., Strahan, E. J., MacCllum, R., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272-299. https://doi.org/10.1037/1082-989X.4.3.272
Russel, D. W., & Russell, D. W. (2002). In search for underlying dimensions - the use (and abuse) of factor analysis in personality and social psychology bulletin. Personality and Social Psychology Bulletin, 28(2), 1629-1646. https://doi.org/10.1177/014616702237645
Preacher, K. J., & MacCallum, R. C. (2003). Repairing tom swift's electric factor analysis machine. Understanding Statistics, 2, 13-43.
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I am running a PCA in JASP and SPSS with the same settings, however, the PCA in SPSS shows some factors with negative value, while in JASP all of them are positive.
In addition, when running a EFA in JASP, it allows me to provide results with Maximum Loading, whle SPSS does not. JASP goes so far with the EFA that I can choose to extract 3 factors and somehow get the results that one would have expected from previous researches. However, SPSS does not run under Maximum Loading setting, regardless of setting it to 3 factors or Eigenvalue.
Has anyone come across the same problem?
UPDATE: Screenshots were updated. EFA also shows results on SPSS, just without cumulative values, because value(s) are over 1. But why the difference in positive and negative factor loadings between JASP and SPSS.
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Thank you, I found the issues and now it gives me very similar results
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Hypothetically, if I would like to validate a scale and I need to explore its latent factors first with EFA followed by a CFA to validate its structure, do I need a new data set for the CFA? Some argued that randomly spliting one dataset into two is also acceptable. My question is that can I apply EFA on the dataset (with all data included) and then randomly select half of the dataset to conduct a CFA?
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If you already have a series of hypotheses about the number of underlying concepts and the assignment of variables to each of them, then you can skip EFA and go straight to CFA.
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Do I treat polychoric correlations like I would other correlations when reporting zero, low, or high correlations before running EFA on my scale items? Would there be an instance where if two variables were highly correlated or not correlated at all that I would give pause and not include the items in the EFA that I run?
I hope this updated question is a clearer. Thank you.
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The only situations that would potentially raise a concern would be:
1) all (or almost all) correlations are near zero. In that case, factor analysis probably won't make much sense because the items don't have enough "in common" and/or contain too much measurement error (are unreliable).
2) one or more correlation is very close to 1.0 indicating close-to-perfect redundancy of items.
3) The sign of one or more correlation coefficients does not match your theoretical expectations (e.g., sign of correlation is negative even though the relationship is expected to be positive based on theory).
Otherwise, I would simply proceed with the EFA and not worry too much until I see the results :-)
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Hello!
I hope this message finds you well!
I am looking for an experienced psychometric with expertise in conducting factor analyses (EFA & CFA) and item analyses (e.g., inter-item correlation, Spearman-Brown split-half reliability, & the McDonald’s omega value) for the item and scale validation, and knowledge of various regression analyses, who is interested in media psychological studies. I need a hand with the statistical aspects of some of my studies. Please send me a message if you were interested to collaborate.
Many thanks!
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You may contact me, find attached my files on the subject;
(19) (PDF) An Easy Approach to Exploratory Factor Analysis: Marketing Perspective Noor Ul Hadi (researchgate.net)
(19) (PDF) Specifying the Problem of Measurement Models Misspecification in Management Sciences Literature (researchgate.net)
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When designing the questionnaire for EFA, what do I need to keep in mind when it comes to the order of the questions?
More specifically, does the order of the questions need to be completely randomized or is it generally allowed to still ask questions in topic blocks according to potential factors/constructs I have in mind?
Thanks everyone!
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A randomized order of items can have the advantage that it may prevent response styles (such as saying "yes" to every item, skipping items, other careless response styles). When items are arranged according to topic/same attribute, participants may get bored and employ a careless response style, especially when the items are similarly worded. They may also find it easier to figure out what attributes you are trying to measure, which may or may not be desirable for your study.
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For convenience, I collected data from a single large sample for scale development.
and then I randomly split into two samples for EFA and CFA.
In this case, I wondering which sample (total? or CFA sample?) should be evaluated for the criterion validity or reliability of the newly developed scale.
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In general, I am in favor of using as much data as possible for reliability and validity assessment. However, if you choose to split your sample and use the first half of the data for purely exploratory purposes (EFA, determination of the number and nature of factors), I don't find it logical to then combine the data again at the end. It seems more logical to me in that case to only use the second portion of the sample for reliability estimation & validation as I view it as part of the second, "confirmatory" step.
This is one downside of the split-sample approach. You "loose" data/power for the "confirmatory" step. In my view, the exploratory step can often be avoided in scale development. Typically, when we develop new scales, we already have a fairly clear theory about which factor(s) should be measured by which variable/item. If that is true in your case, you may not need to explore the number of factors. In other words, you could avoid EFA altogether and use only CFA on the entire sample (no split) to begin with.
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Hello!
I have a question about the discrepancy between conceptualization and operationalization in my study.
I used the concept named 'multicultural teaching competency'(MTC) (Spanierman et al., 2010). In their paper on validating the MTC scale, they conceptualised MTC as awareness, knowledge, and skills.
But when they processed EFA, CFA, and reliability test, the results showed that only knowledge and skills are two sufficient factors to explain MTC.
The authors explained a few reasons why awareness is not one of the factors.
But how can I justify in my dissertation the discrepancy between their original conceptualisation in which they mentioned MTC is composed of awareness, knowledge, and skills, and the outcome of the study which only knowledge and skills are two sufficient factors for MTC?
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My question would be why do you feel the need to come up with a justification? Should not the authors of the original work have provided such a (hopefully convincing) justification for retaining 3 factors when their empirical analyses supported only 2?
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I know hot to reduce questions with EFA, by I can not do this with CFA
and I can use only JASP
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Hello Teo,
1. One very helpful thing to examine in any CFA is the standardized residuals; which bivariate relationships among your observed variables are poorly estimated by the measurement model you have chosen to evaluate? (Big residuals = poor replication of observed relationships; residuals closer to zero = good replication of observed relationships by the proposed measurement model.)
Large residuals may occur because: (a) your factor/measurement model is inadequate or mis-specified; (b) one or more of the observed variables is of poor technical quality (more on this below); (c) your sample may be atypical in composition and/or too small for accurate estimates of the relationships among the observed variables, to name some of the likely reasons.
2. A second thing to look at, if you're worried about individual variables/items, is the estimated loading on the factor. This may be interpreted as a lower bound of the variable/item reliability (relative to the factor to which it is proposed to relate).
If you square the loadings for all variables/items on a factor, sum the values, then divide by the number of variables/items for that factor, that is the AVE. If you firmly believe that some magic threshold exists, you may certainly check to see whether your data set meets/exceeds this threshold, either for each specific factor or overall. (Note: plenty of texts give guidelines, such as ".50" or ".70", but these are guidelines, and not commandments.)
3. Of course, if you jettison many variables/items as a result of your CFA, then you may well be changing the nature of the factors which can be inferred by the remaining items/variables.
4. If a given CFA fails and you get no insight as to how the proposed model may be improved (say, by the steps above as well as inspecting modification indices), you can always fall back to an EFA to determine whether the variables/items with which you're working seem to have any sensible underlying structure. If not, it's likely back to the drawing board to rethink the variables/items and/or the measurement model.
Good luck with your work
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Would appreciate if anyone could give a clear explanation and if possible suggest reading materials or articles that can help me increase my understanding.
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Nadiah Farhanah Mohamad Fazil, my hunch is that it would be quite permissible to retain items that load, presumably unexpectedly, on a particular factor.
Perhaps the following would provide you with useful information about EFA:
Beavers, A. S., Lounsbury, J. W., Richards, J. K., Huck, S. W., Skolits, G. J., & Esquivel, S. L. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research, and Evaluation, 18(1), 6.
Briggs, S. R., & Cheek, J. M. (1986). The role of factor analysis in the development and evaluation of personality scales. Journal of Personality, 54(1), 106–148. https://doi.org/10.1111/j.1467-6494.1986.tb00391.x
Clark, L. A., & Watson, D. (1995). Constructing validity: Basic issues in objective scale development. Psychological Assessment, 7(3), 309–319. https://doi.org/10.1037/1040-3590.7.3.309
Costello, A. B., & Osborne, J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10, 1–9.
de Winter, J., Dodou, D., & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44(2),147–181. https://doi.org/10.1080/00273170902794206
Fabrigar, L. R., Wegener, D. T., MacCallum, R., C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272—299. https://doi.org/10.1037/1082-989X.4.3.272
Gaskin, C. J., & Happell, B. (2014). On exploratory factor analysis: A review of recent evidence, an assessment of current practice, and recommendations for future use. International Journal of Nursing Studies, 51(3), 511–521. https://doi.org/10.1016/j.ijnurstu.2013.10.005
Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2014). Exploratory factor analysis. In J. F. Hair Jr., W. C. Black, B. J. Babin, & R. E. Anderson (Eds.), Multivariate data analysis (7th ed., pp. 89–149). Pearson.
Hayton, J. C., Allen, D. G., & Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods, 7(2), 191–205. https://doi.org/10.1177/1094428104263675
Howard, M. (2016). A review of exploratory factor analysis (EFA) decisions and overview of current practices: What we are doing and how can we improve? International Journal of Human-Computer Interaction, 32(1), 51–62. http://dx.doi.org/10.1080/10447318.2015.1087664
Matsunaga, M. (2010). How to factor-analyze your data right: Do’s, don’ts, and how-to’s. International Journal of Psychological Research, 3(1), 97–110. https://doi.org/10.21500/20112084.854
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift’s electric factor analysis machine. Understanding Statistics, 2(1), 13–43. https://doi.org/10.1207/S15328031US0201_02
Russell, D. W. (2002). In search of underlying dimensions: The use (and abuse) of factor analysis in Personality and Social Psychology Bulletin. Personality and Social Psychology Bulletin, 28(12), 1629–1646. https://doi.org/10.1177/014616702237645
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Pearson Allyn & Bacon.
Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432–442. https://doi.org/10.1037/0033-2909.99.3.432
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when exactly to use a EFA & CFA
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Hello Dawit,
why test your models? You apply a CFA when you believe (--> model) that a set of manifest variables follows the common factor model. By applying a CFA, you test this set of beliefs. You apply EFA when you believe that there is a some sort factor structuring among your manifest variables (-->model!) but you have no clue how many factors are there and which manifest variables were caused by which factor. Thus an EFA model is still a model in which you make bold (=causal) assumptions but it is much weaker as the CFA model in which you have to be much more explict in your beliefs.
And NEVER confuse with the PCA approach which is a simple statistical data reduction approach. A PCA just technically reduces many manifest variables to a smaller set of dimensions and it works no matter where the correlation among the manifest variables came from (in the E/CFA this is crucial).
HTH
Holger
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I am applying EXPLORATORY FACTOR ANALYSIS to my data and I get the following results using parallel factor analysis:
Parallel analysis suggests that the number of factors = NA and the number of components = 3
Are the component and factor the same or shall I interpret the results that EFA is not possible, only principal component analysis?
By using very simple structure (VSS) I got:
The Velicer MAP achieves a minimum of 0.04 with 6 factors
BIC achieves a minimum of Inf with factors
Sample Size adjusted BIC achieves a minimum of Inf with factors
The scree plot shows 3 factors as suitable. The Exploratory Graph Analysis shows 5 groups.
How many factors shall I use for EFA?
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PCA and factor analysis are not the same. See, for example
It is often the case that different criteria will result in different numbers of factors to be retained. To make a decision, I would also look at the rotated solutions for different numbers of factors to see which solution (if any) makes the most sense in terms of the interpretability of the factors.
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CFA of these factors scores variables done. No Validity issues are there.
My dependent variable is categorical with order.
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Yes, they can be used and yes, they would be considered to be continuous variables.
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I would like to know the minimum sample that we need to do Confimatory Factor Analysis. It is same with EFA or not
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There is no fixed rule that applies to all situations as there are many factors that affect the performance of confirmatory factor models such as the type and size of the factor model, the number and quality (reliability) of the indicators (observed variables), the type of estimator used (e.g., maximum likelihood or weighted least squares), the amount and kind of missing data, etc. Even a sample smaller than N = 200 may be fine for certain types of models/situations. If you want to know for sure, the best way to estimate the required sample size is by simulating your model with the expected parameter values using Monte Carlo simulation techniques. I offer a free workshop on sample-size planning using simulations that you can find here:
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We are developing a measure of compassionate care. We have done a literature review and a Delphi study and come up with a 21 item measure across 6 domains. In a second project, we have looked at the statistical properties. One group of over 300 people completed the 21 item measure. We then reduced the number of items based on a lack of generalisability of two items which we removed, and very high correlations between other items which caused us to remove one of each of the highly correlated pairs (following guidance from Field 2013). We ended up with a 6 item measure and our subsequent EFA showed a one factor solution. A subsequent CFA with a different sample completing the 6 item measure showed it was statistically robust. However, only 4 of the 6 domains which the Delphi identified are now included.
My question is... the measure has gone from 21 items to 6 items and lost 2 domains. Statistically it is robust but it looks less like one might expect a measure of compassionate care to look because several items have been lost (e.g. ones about kindness and caring) and theoretically we have lost 2 of the domains which our Delphi identified. Should we (and could we) try to find a middle ground between the short form questionnaire we ended up with and the original 21 item measure? Maybe by adding back in a few of the original items and redoing the EFA? It would mean the CFA we did wouldn't count for this new hybrid measure, but we could perhaps still use it as a longer form alternative to the short form which we have completed a CFA on, and we could at a later date complete a CFA on the longer form.
Or... should I just be following the stats protocol and not trying to mess about with it just because it doesn't look as we initially expected?
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Hello Lucy,
thinking of "domains" when it comes to common factor models versus index construct it the entry to hell :)
If you think that the 6 domains represent 6 different existing latent entities than, yes, you probably mutilated the original model. If you had a specific structure in mind, I would not have started with an EFA but go directly to a CFA. A non-fitting CFA can nonetheless be improved which actually makes the CFA an exploratory approach. Of course this has implications which can /should be dealt with.
However, it may well be that the 6 facets (a better term as domain) were actually only one factor--hence your 6 item measure may capture this one factor. At the end it is not the theory and assumption that counts but the structure of reality (may it be external or in the mind of respondents).
Perhaps you can be more specific (regarding the topic, facets, items, results). In addition, i did not understand the rationale underlying the procedure of removing items (especially "very high correlations between other items which caused us to remove one of each of the highly correlated pairs") which sounds strange....
Good luck
Holger
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Can i split a factor that has been identified through EFA.
N=102 4 factors have been identified.
However, one of the 4 actually has two different ideas that obviously are factoring together. I am working on trying to explain how they go together but it is very easy to explain them as two separate factors.
When I conduct a Conformatory analysis the model fit is better for them separate. . . but running a confirmatory analysis on the same population of subjects that I conducted the Exploratory analysis on appears to be a frowned upon behavior.
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Eric Orr Performing EFA and CFA on the same dataset serves no use. EFA is used to extract factors for the first time from a dataset, whereas CFA is used to verify factors extracted from a separate dataset.
However, exploratory factor analysis (EFA) is commonly employed to determine a measure's factor structure and to assess its internal reliability. When researchers have no theories regarding the nature of the underlying factor structure of their measure, EFA is frequently advised.
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I am currently working on with my thesis and I admit I am really having problems with presenting EFA and CFA results, respectively. The objective of my thesis is to establish the validity and reliability of a self-made measure. I have already presented and interpreted the EFA results and started with the presentation of CFA results but stuck after presenting the figures of the model and the fit indices. What to present and discuss next? I am asking for an outline so that I could check if i presented the EFA results correctly and in order to proceed with the presentation of my CFA results. Your response is highly appreciated.
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I always suggest Hair's manual...my personal Bible when it comes to statistics and psychometry, especially with EFA and CFA:
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (Eighth edition). Cengage.
Section II, chapter 3
Section V, chapter 10
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Are EFA and CCA required for the validity of formative scale?
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Hello Nambram,
beyond what Christian said, the question arises whether validity (in its essential meaning) can be applied to formative constructs.
There is a huge and very confusing literature on "formative constructs" with some people perceiving the construct it self as a latent variable, represenging a truly existing attribute and others perceiving it as formation of facets. The former however, would imply that you can also measure this latent variable by reflective indicators. This was emphasized by Howell et al. (2007). This reflective measurement as well as other variables covarying or causing / resulting the latent variable would provide a basis of evaluating the validity.
In constrast, when you have the conceptualization of the construct as an umbrella term of facets or a composite then the construct isn't a real entity and hence the concept of validity does not exist as your definition as a researcher would determine its meaning and demarkations (see, Borsboom et al., 2003)
HTH
Holger
Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203-219.
Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Reconsidering formative measurement. Psychological Methods, 12(2), 205-218.
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Is EFA and CFA required for validity in case of Formative scale , which I will be doing PLS SEM?Thank you in advance
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Factor analysis implies reflective measurement models where the factors are the causes of the indicators. Therefore, factor analysis is not an appropriate technique for "formative" scales. You would have to validate the scales in some other way.
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Hi, everyone!
I just received the comments of a reviewer who said:
you conducted EFA and based on EFA results, run the SEM modeling. You are supposed to conduct a CFA to confirm the EFA results and finalize the measurement model before proceeding SEM. You can fairly use half of the sample to test EFA and another half to test CFA.
Actually, in my study, i used the EFA to explore the possible dimensions of the high-order constructs, and then build a PLS-SEM with the results of EFA. However, i don´t think I should do also the CFA.
So, how can I answer the reviewer ? and is my method wrong??
Thanks!!!
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I have also come across this situation. In one of my papers, I used EFA and then the structural model. Recently received review comments that I should run CFA. The reviewers recommended that if you have a valid scale to measure then you should run CFA must. EFA can only run under the exploration stage only. As many experts have already answered this question, let me ask a little more about this:
1. When reliability and validity can be checked by Cronbach alpha and expert validity, still is it mandatory to run CFA to check validity and reliability?
2. If exploratory research extracts factors with their items and loadings, why do we further need to run CFA?
Looking forward to hearing from experts.
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Firstly, I developed an index (low, moderate, and high). For index development, I have first taken four indicators with several items with different categories. After running EFA, which has loading .5, I have used those variables to create an index. Now I want to know, can I perform CFA for variables having different categories ( like, one variable has 3 categories, some have four, some have two)? Or Are there any other methods? thanks a lot .
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Christian Geiser thanks Sir...
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Hi all,
I'm validating a tool after translation and have a technical question.
I'll do confirmatory factor analysis (CFA) to test the goodness of the model fit. Previous studies conducted exploratory factor analysis (EFA) or principal component analysis (PCA), but didn't come up with consistent structure matrix of the tool. My questions are:
1. Is it appropriate to do PCA only (without factor analysis) to identify structure matrix? If doing PCA only is adequate, do I still need to split sample into half for PCA and CFA? Are there any papers to support the choice?
2. If conducting an EFA is necessary, can I still choose 'PCA' as Extraction ? Or I should choose 'Maximum Likelihood' as a factor analysis?
Many thanks!
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Hello Xiaoyi,
The short answer is yes, you may split a sample and use part of it for developing a proposed factor model and the held-out portion to run a confirmatory factor analysis.
You may wish to re-think the choice of using PCA as the extraction method for the exploratory phase. It presumes all observed variance is common variance, and that variable-specific variance and error variance do not exist (two presumptions which are seldom true in any research involving human performance or judgment. As well, PCA tends to bias estimated loadings upwards, so your CFA might yield contrary results simply because of this tendency (let alone sampling variation and other influences). Finally, since most covariance-based CFA programs are using maximum likelihood estimation for measurement model parameters, it might be wise to follow a similar extraction method during the EFA phase.
Good luck with your work.
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I performed 200 dental implant procedures, corresponding to 4 implants in 50 patients. How could I control the effect of this variable in my structural equation modelling if it does not follow the non-independence assumption?
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Your options to account for clustered data are to use (1) multilevel modeling (e.g., ANALYSIS: TYPE = TWOLEVEL in Mplus) or (2) TYPE = COMPLEX in Mplus which provides an adjustment of the standard errors and goodness-of-fit statistics with multilevel (clustered) data.
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I am conducting an EFA for a big sample and nearly 100 variables, but no matter what I do, the determinant keeps its ~0 value.
What should I do now?
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Hello Assia,
When computed for a correlation matrix, the determinant may range from 0 (no independent variation) to 1 (no relationship among the variables at all). Lower values generally would suggest the data set _does_ share common variance, and therefore may be amenable to factoring.
A variable set with a determinant of exactly zero would indicate that all variables were isomorphic and interchangeable (one gives exactly the same information as any other). While you could contrive such a data set (for example, asking adults their age four times in a row, and treating the responses as separate variables), it should be apparent that scores on the variables should correlate perfectly (hence, a zero determinant for the matrix).
Good luck with your work.
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Hello,
I intend to develop a social scale that can be used in conjunction with other dimensions of a modular framework.
Reading the literature, I found three potential social dimensions. I conducted a focus group and came up with 7, 8, and 12 items for them.
Similar to other scales developed for the aforementioned framework, I ran three separate EFAs and retained one factor for the first two dimensions each with 4 items.
The third dimension (with 12 items) retained two factors. However, there was one item with cross-loading of 0.387 and 0.390 for two factors (CLS, BRZ). I know I should have removed it, but I kept this item for the second factor because I wanted to have the 4-item format for all the dimensions, and theoretically, it makes sense based on the items.
I have collected another sample to conduct CFA. It does not give great goodness of fit indices but my main problem is the high correlation between the two factors I mentioned above (0.91). My understanding of another thread in researchgate is that one can use second-order CFA to solve discriminant validity of highly correlated factors. Is it correct? Can I do it?
You can see the AMOS results attached.
One more question: in case I delete one factor altogether should I go back and repeat the EFA or I can continue with the 3 factors.
Thank you
P.S: I am not very knowledgeable in statistics so I would be grateful if you could explain it a little. Thank you
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A second-order factor does not "solve" the issue of two or more factors being highly correlated. It merely allows you to "model" this correlation. The more important thing for you to think about is why the two factors are so highly correlated. For example: Could the high correlation be due to shared item content? Are those really two distinct dimensions or could they be summarized into a single dimension?
Also, you mention that the model(s) showed a suboptimal fit. This should be addressed first because a non-fitting model may result in biased (incorrect) parameter estimates that could be misleading. For example, the high factor correlation of .91 may in part be a result of model misspecification (e.g., omitted cross-loadings).
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Hi,
I have conducted an EFA on three items, and all items load on one factor. I then ran a reliability analysis with the three variables to ensure internal reliability using Chronbachs Alpha.
My question: Should I run a reliability analysis before or after the EFA?
Does the order really matter in this case?
Thank you in advance!
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I believe you are supposed to run a reliability analysis after the EFA since if you did it before you might be determining the consistency of the sample results for variables which show items which are loading on the wrong factors or cross-loading on multiple factors, and these factors need to be deleted. For further information click the following link chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://files.eric.ed.gov/fulltext/EJ1085767.pdf
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Hello,
Using EFA I developed a social scale with 4 factors each having 4 items. In a new round of data collection I collected three separate samples (150 each) to test if my new scale can show the differences in social ratings between three different product categories. My question (considering the results belong to three different types of products with various levels of social features): 1- Can I use the 450 responses combined for CFA? 2- Should I use them separately (i.e. three CFAs)? What if the model doesn't fit for one of them? Thank you
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Dear Ehsan Mortazavi,
From my point of view: yes, you can use both samples together and conduct an invariance analysis between A-B, B-C and A-C. It will answer you if the instrument does not fit any sample. The point is: one thing is knowing whether the general structure of the instrument fits the sample. The second is related to the endorsement magnitude of the sample of each item and factor. Generally speaking, the instruments used to fit different samples, unless they are different from each other (as in the WEIRD discussion).
Here is some material that could help regarding invariance:
Hirschfeld, G., & Von Brachel, R. (2014). Multiple-Group confirmatory factor analysis in R – A tutorial in measurement invariance with continuous and ordinal. Practical Assessment, Research & Evaluation, 19(7), 1–11.
Fischer, R., & Karl, J. A. (2019). A Primer to (Cross-Cultural) Multi-Group Invariance Testing Possibilities in R. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.01507
Lugtig, P., & Hox, J. (2012). Developmetrics A checklist for testing measurement invariance. European Journal of Developmental Psychology, 9(4), 486–492.
Some material regarding WEIRD:
Henrich, J., Heine, S. J., & Norenzayan, A. (2010). The weirdest people in the world? Behavioral and Brain Sciences, 33(2–3), 1–75. https://doi.org/10.1017/S0140525X0999152X
Muthukrishna, M., Bell, A. V, Henrich, J., Curtin, C. M., Gedranovich, A., McInerney, J., & Thue, B. (2020). Beyond Western, Educated, Industrial, Rich, and Democratic (WEIRD) Psychology: Measuring and Mapping Scales of Cultural and Psychological Distance. Psychological Science, 31(6), 678–701. https://doi.org/10.1177/0956797620916782
I hope it will help.
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Hi,
I did an EFA with oblimin rotation in RStudio, because I would like to know the factor correlations.
Input:
#EFA for 5 factors, oblimin
out.efa<-factanal(na.omit(p1N[,1:20]),factors=5,rotation = "oblimin")
print(out.efa, cutoff=0)
This was the output:
Factor Correlations:
Factor2 Factor1 Factor4 Factor5 Factor3
Factor2 1.000
Factor1 -0.293 1.000
Factor4 -0.400 0.309 1.000
Factor5 -0.267 0.267 0.458 1.000
Factor3 0.467 -0.322 -0.411 -0.368 1.000
Then, I also wanted to know the factor correlations between these 5 factors and a single item factor. So I computed new factors based on the output of the EFA. I used spss to calculate the correlations, with the following syntax:
Input:
CORRELATIONS
/VARIABLES= f1 f2 f3 f4 ef5 Sitem
/PRINT=TWOTAIL NOSIG FULL
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE.
NONPAR CORR
/VARIABLES= f1 f2 f3 f4 f5 Sitem
/PRINT=SPEARMAN TWOTAIL NOSIG FULL
/MISSING=PAIRWISE.
Output:
Factor Correlations:
Factor1 Factor2 Factor3 Factor4 Factor5 Sitem
Factor1 1.000
Factor2 .33** 1.000
Factor3 .39** .43** 1.000
Factor4 .48** .53** .50** 1.000
Factor5 .33** .34** .49** .49** 1.000
Sitem .49** .50** .55** .57** .50** 1.00
** Pearson correlation is significant at the 0.01 level (2-tailed).
(I also did spearman but factor correlations did not differ much).
Why is it possible that the factor correlations of the second output is different from the first output? Does it have to do with standardisation?
How should I interpret the factor correlations? / which factor correlations should I report?
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I would recommend doing all your analyses in either R or SPSS, which would eliminate one source of "variation."
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Why negative factor loadings in EFA? Even re-coding of the items is also not working. It makes other items to be negative. Why & how to interpret it?
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@Rhianon Allen thank you so much for your reply.
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How can all these discrepancies be explained mathematically?
I am working with a scale that could be considered to have 11 dichotomous (0-1) and polytomous (0-2, 0-3, and 0-5) items OR 20 sub-items (dichotomous and some polytomous). The sample size is sound (> 700 subjects).
A) If I do an exploratory analysis* with 11 items on half of the (randomized) sample, I get 2 factors. The confirmatory analysis** with the other half confirms the two factors, presenting good adequacy indices values. Some authors also obtained 2 factors, either with similar or different methodology (including item-theory analyses).
B) Moreover, I also tested unidimensionality as some found only 1 factor. Again, all indices are adequate (ECVI slightly higher).
C) However, if I do an exploratory analysis* with the 20 sub-items (similarly to other authors), I get 4 factors. Additionally, just out of curiosity, in the total sample, I get 5 factors!
E) There have also been 3, 4, and 5-factor solutions in the literature, either with 11, 20, or 30 sub-items (all dichotomous).
* Unrotated EFA; maximum likelihood extraction; eigenvalues > 1; based on tetrachoric correlation matrix followed by an oblique rotation (promax).
** CFA with the Diagonally Weighted Least Squares method.
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I don't quite understand why the same scale would have 11 or 20 items, but it is not surprising to me that with more items, you could "find" more factors. With more items, there is more room for additional factors (e.g., specific or method factors) to be measured and identified. The more items you use, the more likely it is that some of them will reflect something that is at least slightly different or "unique" relative to the other items. Likewise, with a larger sample size, you have more power to reject models with fewer factors.
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Hi,
I performed PCA on dataset of small sample of 67 people and reduced my variables from 42 to 16. Then I collected responses from 231 people on those 16 variables. I want to perform CFA and then cluster analysis on it. I want to know Do I need to perform EFA before conducting CFA analysis on it? because if I conduct EFA analysis on it again the variable count reduces again. Your guidance please.
Kind Regards,
Ali Abbas
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To add to the other answers on this topic I would carefully consider what the theory says to support your data reduction. Data reduction just based on the data is atheoretical and theory should be used to help you reduce the number of variables.
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Hi
I have to conduct EFA for the pilot study but my sample is 60 with 41 items.
I cant run EFA as it says the sample size is inadquate.
what could be the solution?
I cant increase my sample size for the pilot study.
I read below references
Hair et al (1998) give rules of thumb for assessing the practical significance of standardised factor loadings as denoted by either the component coefficients in the case of principal components, the factor matrix (in a single factor model or an uncorrelated multiple factor model) or the pattern matrix (in a correlated multiple factor model).
On the other hand Field (2005) advocates the suggestion of Guadagnoli & Velicer (1988) to regard a factor as reliable if it has four or more loadings of at least 0.6 regardless of sample size. Stevens (1992) suggests using a cut-off of 0.4, irrespective of sample size, for interpretative purposes. When the items have different frequency distributions Tabachnick and Fidell (2007) follow Comrey and Lee (1992) in suggesting using more stringent cut-offs going from 0.32 (poor), 0.45 (fair), 0.55 (good), 0.63 (very good) or 0.71 (excellent).
MacCallum et al. (1999, 2001) advocate that all items in a factor model should have communalities of over 0.60 or an average communality of 0.7 to justify performing a factor analysis with small sample sizes.
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Khurram Memon, sorry for not being clear. By "limited distribution", I meant a narrow range of responses, e.g., all or nearly all participants responding with something such as Always, Never, Strongly disagree, or Strongly agree.
Does that make sense now?
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For my study , I am taking an already established questionnaire. EFA is used when factor structure has to established for the new scale.With well established factor structure , generally CFA is used for testing the established questionnaires . I have done pilot study where I have collected the data using full length questionnaire. However I wish to delete some items in this already etsbalished questionnaire so as to shrink the length of questionnaire for the conveneience of futurerespondents. So should I go for EFA or CFA for the items deletion?
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Hello Himani,
If your purpose is to create a short form of an established measure, there are various approaches you can elect to take. You could collect responses to the measure from your target population, then consider:
1. Deleting items to maximize internal consistency score reliability (for a given target length);
2. Deleting items to maximize score correlation with some plausible, external variable (e.g., to maximize convergent validity).
3. Deleting items to maximize average shared variance between items and factors, by dropping items with lower loadings.
There are problems with these approaches:
1. You're likely to overfit the resultant short form, so that it appears to "work" well with the data you've collected. However, that's no guarantee that you'll see similarly desirable results with another sample (so, validation via additional data is a must).
2. Maximizing score reliability may change the criterion-related validity of the measure, or its subscores/factors. The same is true for attempting to maximize subscore/factor validity, by dropping items with lower item-factor loadings.
3. Maximizing either score validity or reliability via selective jettisoning of items may alter the qualitative nature of the subscores/factors from what was originally intended by the developers.
But, it's your choice. Just be clear about what you're doing and why you're doing it, and collect sufficient data to allow for validation of your abbreviated version of the measure. I'd use CFA as the validation step.
Good luck with your work.
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Dear all,
I am conducting research on the impact of blockchain traceability for charitable donations on donation intentions (experimental design with multiple conditions, i.e., no traceability vs. blockchain traceability).
One scale/factor measures “likelihood to donate” consisting of 3 items (dependent variable).
Another ”trust” factor, consisting of 4 items (potential mediator).
And a scale “prior blockchain knowledge” consisting of 4 items (control).
All factors/items are taken from previous research.
The first two (hypothesized) factors are measured on a 7 point Likert scale, ranging from 1 (Strongly disagree) to 7 (Strongly agree). However, the “prior blockchain knowledge” contains of 4 items that are measured as a semantical differential from -3 to +3. Essentially, all items in my study thus have the same “scale length” of 7.
My question is: if I perform an EFA/PCA on this data, is this a problem? Is there any gain in recoding the semantical differential to 1-7 after conducting the survey but before EFA/CFA. Or is this unnecessary or even problematic?
Curios to read your ideas, thank you in advance!
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Well that sounds like more of a theoretical question but recoding the -3,3 scale to a 1,7 scale won’t change the interpretation. I don’t think there’s a problem with using EFA to measure a latent factor that causes people to associate the semantic differential item more or less with whatever the thing is. As long as you believe theoretically that there is a latent cause to how people respond to the 4 items. PCA is also fine if your goal is to reduce the information from the 4 items to a single dimension for example. So I think you can go ahead with your EFA or PCA as long as the usual empirical and theoretical assumptions are met
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Hi there, I definitely do need your help!!! Looking through studies and books I got a little confused by the different approaches used to conduct factor analyses for reflective scales before running PLS-analysis. Some recommend carrying out exploratory factor analysis (EFA) using SPSS first, followed by covariance-based confirmatory factor analysis (CB-CFA) using e.g. AMOS. The "stepwise" received results (items) are then applied to PLS for further analyses. Others are pro EFA (in SPSS) but advice against using CB-CFA (e.g. AMOS) before PLS-analysis, criticizing they have different underlying assumptions. Instead they recommend doing the CFA directly in PLS (using the EFA's results). But even within the field of EFA there seems to be some confusion about what extraction method (principal component vs. principal axis vs. ...) and which rotation procedure (oblique vs. Varimax) are most appropriate when using PLS afterwards. So, my question: Are there any rules or is there a generally accepted way of how to conduct EFA and CFA when using PLS? Could you provide me with corresponding references (published articles etc.)? Hope, someone can help! Thanks in advance!
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Dear Yinan Li
Please see Table 1 and relevant studies/stages in the following recently published JR article. The article also provides an extensive web appendix, which should help you with EFA and CFA in a PLS-SEM based study. Please note that this is an open/free access article. Good luck!
Syed Mahmudur Rahman, Jamie Carlson, Siegfried P. Gudergan, Martin Wetzels, Dhruv Grewal. (2022). Perceived Omnichannel Customer Experience (OCX): Concept, measurement, and impact. Journal of Retailing, https://doi.org/10.1016/j.jretai.2022.03.003
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Total variance tells how much variance is explained by all factors. However, if we want to know how much of it is explained by each factor, what is the process?
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All factors in factor analysis amount to 100% variance using SPSS. Those new factors with an eigenvalues above 1 have a sum of variance of above 50%.
However, in social sciences, no set of factors can measure 100% variance and I wonder how the above is reliable. I know in Structural Equation Modeling, no set of factors can explain 100% variance. There is always an error term.
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I am aware that a high degree of normality in the data is desirable when maximum likelihood (ML) is chosen as the extraction method in EFA and that the constraint of normality is less important if principal axis factoring (PAF) is used as the method of extraction.
However, we have a couple of items in which the data are highly skewed to the left (i.e., there are very few responses at the low end of the response continuum). Does that put the validity of our EFAs at risk even if we use PAF?
This is a salient issue in some current research I'm involved in because the two items are among a very small number of items that we would like, if possible, to load on one of our anticipated factors.
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Christian and Ali, thanks for your posts. Appreciated. I'll follow up on both of them.
Robert
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Dear researchers
I developed a scale with 6 items and I want to compare it with a widely used scale with 4 items. These two scales have similar validity, reliability and in the EFA they are loading on the same factor. In addition, I have done a CFA between these two scales (or better said between these two latent variables) and the correlation among them is 1. Finally, another CFA between two other latent variables and these scales, (CFA was done separately that is one at a a time) and the correlations between the latent variables and the scales were similar - not identical though.
Are there any suggestions on how I should work ?
Thank you
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Strictly speaking, it depends on what exactly you mean by "equivalent" because there are different levels and definitions of "equivalence" of latent variables in measurement theory, for example, tau equivalence versus essential tau equivalence versus tau congenericity in classical test theory.
"Less strictly speaking" (which may be enough for the purposes of your study), if you can demonstrate that the observed variables in question load highly on the same factor in a CFA or EFA and/or that two factors for these item sets are perfectly or close to perfectly correlated (like you have already done), then I would say it's fairly plausible that these variables measure very similar attributes or even the exact same attribute.
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Dear all,
I am conducting research on the impact of blockchain traceability for charitable donations on donation intentions (experimental design with multiple conditions, i.e., no traceability vs. blockchain traceability).
One scale/factor measures “likelihood to donate” consisting of 3 items (dependent variable).
Another ”trust” factor, consisting of 4 items (potential mediator).
Furthermore, a “perception of quality” consisting of 2 items (control).
And a scale “prior blockchain knowledge” consisting of 4 items (control).
My question is: since all these scales are taken from prior research, is CFA sufficient? Or, since the factors are from different studies (and thus have never been used together in one survey/model) should I start out with an EFA?
For instance, I am concerned that one (or perhaps both) items of ”perception of charity quality” might also load on the “trust”-scale. e.g., the item “I am confident that this charity uses money wisely”
Curious to hear your opinions on this, thank you in advance!
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Kim Fleche, I'm glad my post was helpful. Please be aware that coefficient alpha (often less appropriately referred to as Cronbach's alpha) is a much more complex, uninformative, and deceptive metric than many researchers seem to appreciate.
A major feature of coefficient alpha is that it is highly dependent on the number of items involved. Because of that, a small number of nicely correlated items can have quite a low coefficient alpha. Conversely, by the time there are 20 or more items, the value of alpha can be quite high despite little association between many of those items.
The following publications might be helpful:
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One of my constructs around knowledge did not load as a single construct during EFA. It loaded as a number of constructs. Just wondering what is the best way to report that within a thesis? Additionally, can you discuss scale items of this construct within the findings and discussion chapters? There is a lot of rich data from these responses, it just cannot answer the hypothesis.
I would really appreciate some guidance. Thank you for any advice.
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In addition to what Dr. Geiser mentioned, if there is a good theoretical basis for one general factor, it is possible to consider it as a second-order factor, on which all first-order factors load.
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Hi...I have 7 constructs to be measured in my study. Three constructs are adopting the items from the established scales and the remaining constructs are adapting scales from the previous studies. My question is, should I run the EFA only to the adapted scales or to both adapted and adopted scales that I used in my study?
Thank you in advance for your help.
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I beg to differ from Subhankar Banerjee 's suggestion. You speak of established scales and previous studies so there is a degree of certainty of which items belong to which factor. Judging from the information you have provided, I would prefer CFA over EFA.
Best
Marcel
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Hello Guys,
I'm performing factor analysis in SPSS with 168 observations of likert-scale variables, EFA generates two factors, thus Factor 1 includes 3 variables and loading scores are high (0.777, 0.785, 0.421) and so the composite realibility and extracted variance, around 0.8. However, cronbach Alpha for internal consistency showed value of only 0.52.
The Factor 2 showed good values for all three measures, so the only problem is internal consistency of the Factor 1. The discriminant validity between two factor is also good. KMO of whole construct is around 0.75.
In this case, can I consider this "problematic" factor as "valid"? Otherwise, what can I do to solve this issue?
The idea is to use them within Structural Equation Modelling later. Thank to all of you in advance!
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Andrei Mikhailov Cronbach's alpha is a meaningful measure of composite reliability (reliability of the sum or average of measures) only under the assumption of (at least) essential tau equivalence as defined in classical test theory (CTT). Essential tau-equivalence means your items are (1) unidimensional (i.e., they measure only one factor with uncorrelated error variables) and (2) have equal weights on that single factor (equal unstandardized factor loadings, no cross-loadings onto other factors). These assumptions cannot be tested with EFA, but they can be tested with confirmatory factor analysis (CFA). When the measures do not satisfy these criteria, Cronbach's alpha may be underestimating their composite reliability and/or may be completely misleading as a measure of composite reliability. Alpha also implies that your measures are continuous (measured on an interval scale).
Alpha itself is not a measure of unidimensionality or homogeneity. It can be high or low for item sets that are uni- or multidimensional. I personally therefore find the term "internal consistency" to be problematic because it suggests that alpha can tell you how homogeneous your items are (which is not the case). Alpha really is a measure of composite reliability under the assumptions given above--not more and not less.
In addition, I would be skeptical about the item with the rather low (standardized?) loading (.421). Often, such a low loading suggests that this item measures something different from the others, at least in part. What do the cross-loadings of the items look like in the EFA solution? And did you use EFA or PCA?
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My factor loadings are showing 3 factors when it is done with Eigenvalues in the SPSS. Now I fixed the number of factors to the equal number of variables in the study and the EFA results come satisfactory without any cross-loadings.
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Belal Edries Thanks a lot for your detailed and comprehensive reply. I tried to get some references from the literature but could not find any example where the number of factors increased after the factor analysis and the researcher kept the extra factors in his/her scale. So I think I should adopt the 2nd option (as per your reply) i,e, stick with the initial 4 dimensions. Thanks
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Can I compare eigenvalues from PAF (EFA) of data with eigenvalues of Parallel analysis (PCA not factor approach) to extract the components in spss? If yes kindly provide me a reference to support the argument.
Kind regards,
Ali Abbas
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Hi,
Can we run CFA analysis on the questionnaire that its item has been translated, deleted, and validated using EFA?
Originally, the questionnaire has 25 items. It has been translated and were tested on an adult sample. Using EFA analysis, the questionnaire has a 3-factor model and 5 items were removed from the questionnaire.
Currently, I am planning to conduct CFA on those 20 items. Am I doing it correctly? Because I'm using an adolescent sample. I figured out that in past research that uses adolescent samples (from different countries), they test again on 25 items and consistently found a 4-factor model (some used EFA, and some used CFA).
What if I just test the 20 items on the adolescent sample without reanalyzing the 25 items?
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Hello Afrina,
The first order of business is to determine which model it is you're trying to confirm for a translated version of a questionnaire (using an adolescent sample):
A. The 4-factor model, based on the full (25-item) version of the instrument, or
B. The 3-factor model, based on the reduced (20-item) version of the instrument.
Then proceed from there.
You won't be able to say much about the 4-factor model if you evaluate the reduced version of the instrument.
Good luck with your work.
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Respected Researchers,
I am working on urban sustainability and my final objective is to propose a framework of urban sustainability. In this regard, I have used EFA first and want to use CFA, but I got to know that SEM has two methods i.e., CB-SEM and PLS-SEM. If I do not use CB-SEM or PLS-SEM, can I use just CFA in my study? If I can use it, please recommend me the procedures for conducting CFA.
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In addition to the above answer, after conducting EFA (generally using SPSS), the next step i.e. CFA can be done via AMOS graphics which is an add-on for SPSS. It is relatively simple to perform, and there are tons of YouTube tutorials also available.
I personally would recommend this link
The instructions are very clear, and generally for CFI, the chi square value, GFI, AGFI, CFI, NFI, TFI, RMSEA etc values should be within the specified values. Below is the link for reference of values. It is important to note that for samples more then 200, the chi square value might not be of significant value.
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Is it fair to compare findings from studies where one study has used PCA and the other EFA when the measure is unidimensional?
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Hello Prudence,
Neil Gorsuch wrote on this a long time ago.
If you compare PCA with principal axis factoring (a popular extraction method in common factor analysis), you'll tend to find that PCA yields stronger estimated loadings than common factor analysis, unless the number of variables involved is large. In your case, nine variables is not a large number.
I'd like to opine about Marcel's observation about the high rate of use of PCA in the literature, when common factor analysis would likely have been the better choice. A lot of folks lay the blame for this on SPSS (and similar software packages), in which the default extraction method for the "factoring" subprogram is principal components analysis. I suspect a lot of users probably didn't know better or even attend to the fact that this was the case.
Good luck with your work.
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I`m conducting the translation of a very short scale of 12 ítems to assess therapeutic alliance in children. I have 61 answers and I wonder if that number of subjects it`s acceptable to run Exploratory Factor Analysis. I know that there is a suggestion of 5 participants for item to do EFA and 10 participants for item to do CFA. However, the number of participants here seem to be very smal for these analysys. What it´s your opinion?
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Hello Leandro,
The vague answer is, more cases is generally better than fewer cases. There are two reasons:
1. The factor model you seek must, ideally, be capable of providing good estimates for the (12*11/2 =) 66 unique observed relationships among your 12 variables (here, item scores). That's a lot to ask of 61 cases.
2. In general, the smaller the N of cases, the more volatile are the observed relationships among the variables from sample to sample. Hence, the less likely that your sample data will accurately represent the correlations that may exist in the population. As these correlations are what the EFA is intended to account for, if they are incorrect then you likely will identify a factor model that does not generalize well to the population. The literature is full of studies in which one set of authors using a small or modest sample claims their EFA shows "different" results than those from another set of authors, even if ostensibly drawing from the same population.
Can you still proceed? Yes, of course--the numbers won't leap up from your data file and protest! However, do be mindful that: (a) guidelines such as "at least 100 cases" and "10-20 cases per variable" for EFA abound; and (b) you likely would want to characterize your results as tentative or exploratory, rather than as a definitive solution to the question of the true factor structure.
Good luck with your work.
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Hello everyone
How can I statically validate a translated sleep questionnaire with small sample (n=30 maybe more)?
- I have no access to previous Valid questionnaire used in the same population or to a clinical sample to verify discriminative validity.
Someone advised me to use Bayesian Factor Analysis, if it's possible to do CFA using Bayesian with this sample size can you recommend any books on the matter.
thank you.
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Hello Aziz,
So, very small sample, no other measures administered so as to inform concerning convergent/discriminant validity, and you want to establish evidence for validity of a translated measure, right? Well, we all prefer a challenge!
1. There is evidence that Bayesian CFA can function well with smaller-than-usual data sets, but B-CFA is hardly a simple matter (see this link: ).
2. Proponents of PLS-SEM claim that small N can still be profitably used to evaluate factor models (have a look at this link: https://www.sciencedirect.com/science/article/abs/pii/S0148296319307441)
I suspect that an N of 30 likely strains the bounds of credibility no matter what method you might apply, in the realm of CFA (especially if your measure has any appreciable number of items). However, I can appreciate that there are times when you simply have to forge ahead with whatever data you are able to collect. You might be wise to characterize the results as "tentative," or "exploratory," rather than as definitive for your target population.
Good luck with your work.
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I have translated an SEL scale from English to Urdu in the Pakistani population. suggest better ways to establish its psychometrics' properties. In the initial analysis, EFA shows a different factor structure than the original scale.
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There is bad idea that conduct EFA and a CFA on the same data.
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Dear experts,
I would like to know whether it is okay/possible to develop two models (one based on theoretical evaluation and another based on theory development). Like for example, I have developed a questionnaire based on a model. Now I have two processes. process 1) EFA (Quartimax- that yielded the same result as the model) CFA for confirming the model and SEM for Model testing. this helps me in evaluating my theory. I also want to know if there are any hidden factors or maybe I might get a better model so theory development based on scientific numbers. So Process 2) EFA based on Parallel analysis- varimax, CFA, and Model 2 SEM.
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You can develop n number of models from data. :)
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Exploratory factor analysis was conducted to determine the underlying constructs of the questionnaire. The results show the % variance explained by each factor. What does % variance mean in EFA? How to interpret the results? How can I explain the % variance to a non-technical person in simple non-statistical language?
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The % variance explained by a factor in a given variable is often called communality (h^2). It gives the proportion of individual differences in an observed (measured) variable that is accounted for by the common factor. The communality is similar to R-squared in regression, except that the independent variable is a latent factor. Under certain conditions, the communality is equal to the reliability of a variable, namely when the variable only measures the common factor and measurement error.
In summary, the communality gives you an estimate of a variable's ability to reliably measure the common factor. The closer the communality to 1, the more reliable the variable as a measure of the factor.
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Hi, I have done EFA on a questionnaire. Initially, there was a total of 16 variables. After EFA I extracted two components with 8 variables.
My total variance explained appears to be 55.9%, all communalities are > 0.4 and KMO is 0.689. If I further delete the items to increase the TVE above 60% only 6 variables are left with 2 components and two of my highly important are deleted. Now, first of all, I would like to ask if TVE of 55.9% is acceptable (My work is survey-based from Industry).
Secondly I am using direct oblimin rotation, Do i need to report only pattern matrix in my paper as I have also performed CFA and cluster analysis.
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Hello Ali,
There's a lot to unpack in your query, so please excuse the list-type response.
1. Variance accounted for is typically not the best criterion to use in deciding upon a factor solution. One common exception would be that of generating linear composites that are orthogonal so as to overcome issues with collinearity.
2. I would be more concerned with how it was that an otherwise thoughtfully-developed set of 16 variables (probably individual questions on a survey form) somehow ended up being winnowed down to 6 (or 8, depending on your stopping rule for extraction and salience criterion). That would suggest a need for better conceptualization of the target attributes the survey was intended to measure.
3. You didn't indicate what stopping rule you used for ending factor/component extraction. I suspect it may have been the eigenvalue > 1 rule. That has been shown to work less well in identifying "true" structure (when data are simulated so that a true structure may be said to be known) compared to other methods, such as parallel analysis or minimum average partial correlation.
4. You mention "components" being extracted, which makes it sound as if you used principal components analysis, not common factor analysis. (Common) factor analysis would be better suited for data such as what you're gathering: perceptions about something or other from workers in industry).
5. Oblique rotation is fine.
6. Yes, do report the pattern matrix. If you subsequently ran a confirmatory analysis on the 6- or 8-variable set (whichever you embraced as the 'answer'), then loadings will be given there. If you're not including the CFA, then do give loadings and proportion of reproduced correlations that were within +/- .05 of the observed values for the data set. The latter gives one indication of how satisfactorily the chosen structure captures information about the relationships among your variables.
7. Is there a minimum threshold for variance accounted for? The answer is generally "No." Further, is the difference between approximately 56% variance accounted for and 60% worth jettisoning 25% of the remaining variables? I doubt it.
There are numerous examples in the literature of measures that author/s present for which initial factoring might yield between 35-60% of variance. These aren't ideal, of course, as that suggests a lot of specific and/or error variance in the data set. However, the resultant factors may still be useful, depending on your specific research aims.
Good luck with your work.
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Data collected using Likert Scale and collecting insights from Experts, entrepreneurs and customers
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In order to do CFA, you have to a prior model that assigns each item to a specific conceptual factor. If you do not have a prior model, then you can use EFA to develop one.
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What are the determinants to measure the effectiveness of customer loyalty programs in the emerging Supermarkets of Bangladesh conducting EFA and using AMOS Software where data has been collected from more than 350 respondents through 5 - Point Likert Scale?
What is the best way to measure effectiveness of customer loyalty programs of supermarkets using AMOS Software?
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your questions are a bit all over the place if you will forgive me for saying so. Please state clearly what it is you want to know. By the looks of it, you have already collected data. "Effectiveness of customer programmes" appears to be your dependent variable. How did you measure it? What are your independent variables? It would be quite helpful if we had a path diagramme illustrating your research questions or hypotheses.
As for your second questions, beta values are regression coefficients that show what happens to Y if X changes by a unit - this is different for binary and continuous variables).
Best
Marcel
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Is the sample size for CFA the same like that of EFA in educational survey research?
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1. 50+8k
k=number of independent variable
or,
2. 10 x number of statements/items
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I translated a scale from Engish to Arabic using the back-translation technique. After collecting data, the scale has a low reliability (α < 0.4), but when one item is removed alpha exceeds 0.7. I suspect this particular item has a translation issue, because the original English scale demonstrated high reliability across many published studies.
So is it right to use EFA or PCA to justify why I removed the troubling item in my research? This particular item does not load on factor 1 but on factor 2 (the orignial scale loads on 1 factor).
Thank you!
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Sultan Sabr Your approach seems very reasonable to me. If your factor analysis clearly shows that the item in question does not load on the intended factor, this may be a reason to exclude (or modify or replace in future studies) that item, particularly if there are also plausible theoretical-substantive reasons (e.g., translation issues) as you write.
Note that exploratory factor analysis (EFA) and PCA are not the same thing (although they often lead to similar conclusions). For details, see, for example
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Hi, I am working on a project about ethical dilemmas. This project requires development of a new questionnaire that should be valid and reliable. We started with collecting the items from the literature (n= 57), performed content validity where irrelevant items were removed (n=46), and piloted it to get the level of internal consistency. Results showed that the questionnaire has a high level of content validity and internal consistency. We were requested to perform exploratory factor analysis to confirm convergent and discriminant validity.
Extraction PCA
rotation varimax
Results: the items' communalities were higher than 0.6.
kMO 70%
Barttlett's test is significant.
Number of extracted factors 11with total explained variance 60%.
My issue is 6 factors contain only 2 items. Should I remove all these items?
With notice that the items are varied, each one describes a different situation, and only they share in that they are ethical dilemmas and deleting them will affect the overall questionnaire ability to assess participants' level of difficulty and frequency of such situations.
EFA is new concept for me; I am really confused by this data.
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Eman ALI Dyab, if you have been asked to conduct exploratory factor analysis (EFA), I suggest you follow that instruction rather than conducting confirmatory factor analysis.
There are other things you should consider, however. Given that your items' communalities are > .60, I think you don't need to abide by the rule of thumb that you have 10 x the number of participants as there are items, but I think you do need to ensure you have enough participants. Maybe 200 would be sufficient.
Also, given that you have 11 factors in the data, I wonder whether you are using the Kaiser criterion to determine the number of factors. That method has been criticised for at least 20 years. A better method is to use the scree test in conjunction with parallel analysis. The scree plot is often quite easy to interpret. I am attaching information about parallel analysis in case that helps.
Apart from that, I think it would be better to use EFA, not PCA (PCA is not really EFA, and you have been asked to conduct EFA, anyhow) and that you use an oblique (e.g., promax), rather than varimax, rotation. (Use of varimax has been criticised for quite a long time - though a lot of researchers keep using it, probably because they blindly follow what the crowd is doing.)
My inclination would be to remove items that load only on two-item factors. However, before doing that, I'd go back and use the scree plot in conjunction with parallel analysis, EFA with an oblique rotation, and a series of EFAs in which poorly performing items were successively removed.
All the best for your research.
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Do you know any renowned article which has been published in Scopus journal describing that for conducting the Exploratory Factor Analysis (EFA), which method is the best, 'Principal component' or 'Principal Axis Factoring ' in SPSS?
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Hi, Mohammad Kamrul Ahsan. Here are some good papers on EFA that I hope will help you.
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding statistics: Statistical issues in psychology, education, and the social sciences, 2(1), 13-43.
Yong, A. G., & Pearce, S. (2013). A beginner’s guide to factor analysis: Focusing on exploratory factor analysis. Tutorials in quantitative methods for psychology, 9(2), 79-94.
Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical assessment, research, and evaluation, 10(1), 7.
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological methods, 4(3), 272.
Williams, B., Onsman, A., & Brown, T. (2010). Exploratory factor analysis: A five-step guide for novices. Australasian journal of paramedicine, 8(3).
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I am running an EFA on an 8-item questionnaire. Each item can be rated between 0 and 10, with higher scores = more negative/worse relative to lower scores. Sample size is small at n=81. I am treating the data as ordinal, so am looking at polychoric correlations. I have done some preliminary analyses but have struck problems as item 7 on the scale has missing response categories (no participants chose 6, 7, 9 or 10) and so polychoric correlations could not be calculated. Must I remove this item for the analysis to work or are there other ways to manage this?
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Employ listwise computation or pairwise deletion by cleaning and removing the offending items, this could be tedious in large item sets.
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I collected 109 responses for 60 indicators to measure the status of urban sustainability as a pilot study. So far I know, I cannot run EFA as 1 indicator required at least 5 responses, but I do not know whether I can run PCA with limited responses? Would you please suggest to me the applicability of PCA or any other possible analysis?
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I would recommend you read about the difference between EFA and PCA first. Whether or not you should run an EFA has nothing to do with the number of response options on the indicators, five or otherwise. In general, EFA is preferable to PCA as it is considered to be the 'real' factor analysis. The are many threads on RG on this issue.
Best
Marcel
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Hi,
One tool that I used showed 4 factors in EFA, however, in CFA, 3 factors were identified as a best goodness of fit. Furthermore, according to the original article that developed the tool also showed 3 factors for the tool.
In this case, even though my EFA showed 4 factors, can I say that the tool has 3 factors in my sample and is valid for my sample?
I need your precious thoughts and opinion.
Thank you so much in advance.
Best regards,
Judy
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Jung Eun Kim My question would be: Given that the a priori theoretical assumption/expectations was that there should be 3 factors (not 4), and given that a 3-factor CFA solution shows an adequate fit for your data, why would you even run an EFA at all?
EFA is typically used for exploring the number of factors when you don't know how many and which factors may be needed. In your case, you had a clear idea about the number of factors from the previous literature before you ran the analyses. Therefore, I would argue that EFA is not needed here and that you should stick with your 3-factor CFA solution if it shows a decent fit and also otherwise meets your expectations in terms of the estimated factor loadings, factor correlations, etc.