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Exploratory Factor Analysis - Science method

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I used confirmatory factor analysis without using the exploratory factor analysis first. The assumption that supported this was the clear presence of the factors in the literature. Is it correct not to go for the exploratory factor analysis and jump directly to CFA when you have clearly established factors in the literature and theory?
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Yes, absolutely. There is no point in "exploring" factors when you have a clear theory or prior knowledge about the factors and how the observed variables (measurements) relate to them. In that case, you want to "confirm" (test) rather than explore/determine the number and nature of the factors. EFA is only needed when you have no prior theory and need to explore or when you have a CFA solution that completely fails to fit and you don't know why.
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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 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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I plan to develop a semi-structured assessment tool and further validate it on a relatively small sample of below 50 (clinical sample). I have been asked by the research committee to consider factor analysis.
So in this context, I wanted to know if anyone has used regularized factor analysis for tool validation which is recommended for small sample sizes?
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The sample size is relatively quite small but if the size is above 100 then you can try. There had been studies who have opted for exploratory factor analysis on such smaller sample. But you got to check the KMO and Bartlett's Test of Sphericity to see the adequacy of your data. Try reading the following research papers who support smaller samples for EFA.
De Winter, J.C.F., Dodou, D., & Wieringa, P.A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44, 147–181.
Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: current approaches and future directions. Psychological Methods, 12, 58-79.
Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815-824.
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Exploratory Factor Analysis and Confirmatory Factor Analysis are used in scale development studies. Rasch Analysis method can also be used in scale development. There are some researchers who consider the Rasch Analysis as up-to-date analysis. Frankly, I don't think so, but is there a feature that makes EFA, CFA or Rasch superior to each other in Likert type scale development?
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Hello Ali,
In general, any instrument should:
1. Measure the target behavior/attribute/perception or construct as intended (and not others);
2. Yield scores that are reliable indicators of status with respect to the target of the measurement; and
3. The items/questions/stimuli clearly communicate the intended task(s) to respondents.
Numerous texts and articles are available that elaborate these points. Your query, though, appears to focus on two specific concerns associated with instrument development:
1. The dimensionality or structure of the measure (related to #1, above), and
2. How to scale the response options (related to #1 and #2, above).
These are not mutually exclusive concerns, especially when one chooses to frame the stimuli as Likert-type response options. Most would rightly consider that framework as yielding ordinal scores. IRT models do offer a way to estimate the thresholds on an interval scale, which is quite helpful.
Dimensionality may be assessed, indirectly, for IRT models, or more directly, via CFA, EFA, or multi-dimensional scaling (MDS). For Likert-type scales, SEM programs like mplus or lavaan (in R) can handle ordinal variables in the assessment of dimensionality.
Finally, Likert himself envisioned summative scores (individual item/stimulus responses added across a set of related items or stimuli) as the usual score of interest, and not so much the individual response (see this reference: https://legacy.voteview.com/pdf/Likert_1932.pdf). This implies that the set of items should be unidimensional.
Good luck with your work.
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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 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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Greetings,
I am a DBA student conducting a study about "Factors Impacting Employee Turnover in the Medical Device Industry in the UAE."
My research model consists of 7 variables, out of which:
  • 5 Variables measured using multi-item scales adapted from literature ex. Perceived External Prestige (6 items), Location (4 items), Flextime (4 items),.. etc.
  • 2 are nominal variables
I want to conduct a reliability analysis using SPSS & I thought I need to do the below?
  1. Conduct reliability test using SPSS Cronbach's alpha for each construct (except for nominal variables)
  2. Deal with low alpha coefficients (how to do so?)
  3. Conduct Exploratory Factor Analysis to test for discriminant validity
Am I thinking right? Attached are my results up to now..
Thank you
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The issue is not my specialty , with my best wishes
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Hi everyone,
I have longitudinal data for the same set of 300 subjects over seven years. Can I use '''year' as a control variable? Initially, I used one way ANOVA and found no significant different across seven years in each construct.
Which approach is more appropriate?. Pooling time series after ANOVA (if not significant) or using 'year' as a control variable?
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I thinking, when there is no significant difference found Through, its improper to use it as control variable. Better is allow PLS to create its own groups if any were present in the data.
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Hello everyone,
As the title suggests, I am trying to figure out how to compute a reduced correlation matrix in R. I am running an Exploratory Factor Analysis using Maximum Likelihood as my extraction method, and am first creating a scree plot as one method to help me determine how many factors to extract. I read in Fabrigar and Wegener's (2012) Exploratory Factor Analysis, from their Understanding Statistics collection, that using a reduced correlation matrix when creating a scree plot for EFA is preferable compared to the unreduced correlation matrix. Any help is appreciated!
Thanks,
Alex
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Take a look at the attached Google search for your answer. Best wishes, David Booth
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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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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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I have good result with low variance explanation (Less than 50%) in exploratory factor analysis, and read some discussions about the acceptable for total variance explanation < 50% in social sciences. Please recommend papers to support this issue or give me your suggestion.
Thanks in advance.
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Hello Sirwarit,
There are a lot of possible answers to your query as it was posted.
1. It could be that the set of variables you are attempting to factor simply do not share common latent variable underpinnings, and therefore no parsimonious factor structure (other than, perhaps, something approaching the "worst case" of k factors for k variables) exists.
2. It could be that the variables are poorly measured and/or suffer from high levels of specificity, such that the common variance is "low," according to your appraisal. Better versions or measurements of the variables might alleviate this problem.
3. You could have extracted too few factors to account for the variation in the variable set. Alternatively, a chunk of the variables in your set simply might not belong in the set, and this is causing your solution(s) to have low variance accounted for.
4. Your judgment that 50% of variance being explained by the factor structure you've selected from your EFA might be too pessimistic. I've seen a lot of published studies in which EFA solutions adopted by author/s account for 35-60 percent of variance. Often, this coincides with author/s' decision to jettison a number of the variables from the solution because of low variable-factor loadings. Are these ideal structures? Probably not, but one of the reasons for engaging in EFA is to refine a variable set into a group which does have common latent underpinnings...so, it is not unreasonable to expect that some variables might not end up being included.
I agree with Imran Anwar that it wasn't clear what you meant by having obtained good results.
Good luck with your work.
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I am using the Environmental Motives Scale in a new population. My sample size is 263.
The results of my exploratory factor analysis showed 2 factors (Eigenvalue>1 and with loadings >0.3) - Biospheric Factor and Human Factor
Cronbach alpha was high for both factors (>0.8)
However, unexpectedly, confirmatory factor analysis showed that the model did not fit well:
RMSEA= 0.126, TLI =0.872 and SRMR = 0.063, AIC = 6786
After a long time on Youtube, I then checked the residual matrix and found that the standardized covariance residuals between two of the items in the Biospheric factor was 7.480. From what I understand if values are >3, it indicates that there may be additional factor/s that are accounting for correlation besides the named factor. I therefore tried covarying the error terms of those two items and rechecked the model fit using CFA.
Results of this model show much better model fit.
RMSEA = 0.083, TLI = 0.945, SRMR = 0.043, AIC = 6731 (not as much difference as I thought there would be)
The questions I am now left with (which google does not seem to have the answer to) are:
1. Is it acceptable to covary the error terms to improve model fit?
2. How does covarying error terms impact on the scoring of the individual scales? Can I still add up the items to measure biospheric vs human scales as I would have without the covarying terms?
I would be so grateful for any insight or assistance.
Thank you
Tabitha
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Tabitha Osler Many software programs for confirmatory factor analysis (CFA) will allow you to estimate and save individual factor scores as new variables to your data set. These scores can then be used in the same way as a conventional scale score (e.g., sum score of items). One advantage of factor scores is that they take the different item loadings into account and that they would allow you to also account for the error correlation parameter when estimating the factor scores.
I'm not sure which software program you're using. In any case, the program manual/user's guide should have information regarding options for estimating and saving factor scores.
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I used exploratory factor analysis for 4 latent variables, the result in the table called "total of variance explained" has "% of variance". is it similar to average variance extracted?
What steps to do discriminant validity in SPSS?  I run the factor analysis, then compute the latent variable to become observed variables, after that I run the correlation. is it the correct process?
Thanks for your attention
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VALUES SHOULD BE GREATER THAN .05
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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 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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Query1)
Can mirt exploratory factor analysis method be used for factor structure for marketing/management research studies because most of the studies that I have gone through are related to education test studies? My objective is to extract factors to be used in subsequent analysis (Regression/SEM) My data is comprised of questions like: Data sample for Rasch Factors Thinking about your general shopping habits, do you ever: a. Buy something online b. Use your cell phone to buy something online c. Watch product review videos online RESPONSE CATEGORIES: Yes = 1 No = 0 Data sample for graded Factors Thinking about ride-hailing services such as Uber or Lyft, do you think the following statements describe them well? a. Are less expensive than taking a taxi c. Use drivers who you would feel safe riding with d. Save their users time and stress e. Are more reliable than taking a taxi or public transportation RESPONSE CATEGORIES: Yes =3 Not sure = 2
No = 1 Query2) If we use mirt exploratory factor analysis using rasch model for dichotomous and graded for polytomous, do these models by default contain tetrachoric correlation for rash model and polychoric correlation for graded models? My objective is to extract factors to be used in subsequent analysis (Regression/SEM) Note: I am using R for data analysis
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I would really appreciate that you spared some time to answer my question. May be I am unable to ask question properly but here my objective is to create factors from underlying battery of items with different scales. So my question is simple that can I use mirt to perform EFA to create factors to be used in subsequent analysis (Regression/SEM).
One more things I would like to know that what exactly "easy" and "difficult" items you mean in your given answer?
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Hi,
I used a self-efficacy tool for my sample. According to the original article, there is only one factor in the tool. However, in the Exploratory factor analysis for my sample, two factors were found. How can I interpret this result?
Thank you so much for your answer in advance!
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Basically, A statistically significant result is not due to chance and is determined by two important variables: sample size and effect size. The sample size refers to the size of the sample for your experiment.
Best Regards
Dr. Fatemeh Khozaei
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Hi, I have run an exploratory factor analysis (principal axis factoring, oblique rotation) on 16 items using a 0.4 threshold. This yielded two factors, which I had anticipated as the survey was constructed to measure two constructs. Two items had factor loadings <0.4 (from Factor 1) so I removed them, leaving 14. However, upon closer inspection, one of the items from Factor 2 loaded on to Factor 1 (|B| = 0.460).
The distinction between the two constructs is very clear so there should not be any misunderstanding on the part of the participants (n = 104). I'm unsure of what to do. I checked the Cronbach's alpha for each factor: Factor 1 (a = .835 with the problematic item, a = .839 without). Factor 2 is a = .791).
Do I remove the item? Any advice would be very much appreciated. Thank you!
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Joanne Lim, I'm glad my post was helpful. The Costello and Osborne article is informative and authoritative. If you want more information about sample sizes for EFA, feel free to ask me.
I think we might have a misunderstanding about communalities versus loadings. In SPSS output, the communalities are provided before the loadings, and it's the extraction communalities you need to pay attention to. I think they need to all be above ~.50 if you want to work with a smallish sample.
Your loadings look OK to me.
You could be spot on when referring to wording of items in your scale possibly not being satisfactory. With regard to the scale that I referred to in my post above, I'd forgotten to mention that a number of the items have wording that I regard as quite unpolished. Some are even silly.
One last note, please don't worry if the coefficient alphas for your two factors are quite low. With as few as 6 or 7 items, the alphas can be quite low (down around .70, maybe a touch less) without cause for concern. Check out the interitem correlations!
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Can anyone help me with the sample size calculation for the exploratory factor analysis? Do you know how to calculate it and with which statistical program? Thank you.
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Fernando Calvo, there are a number of recommendations concerning the desirable sample size for exploratory factor analysis - and they don't always agree with each other.
The simplest recommendation is to aim for 10 times the number of people as there are items to be submitted to EFA. So, if you have 20 items, you'd need 200 people. That's the recommendation in the following chapter:
Dixon, AE. Exploratory factor analysis. In Plitchta SB, Kelvin EA, editors. Munro’s statistical methods for health care research. 6th ed. Philadelphia, PA. Wolters Kluwer; 2013. pp. 371–398.
There are other recommendations, however. My colleagues and I dealt with them in an article we'd had published nearly 2 years ago:
Ma, K., Trevethan, R., & Lu, S. (2019). Measuring teacher sense of efficacy: Insights and recommendations concerning scale design and data analysis from research with preservice and inservice teachers in China. Frontiers of Education in China, 14(4), 612–686. https://doi.org/10.1007/s11516-019-0029-1
It's an open-access article. Check out the middle paragraph on page 628 for several recommendations, and choose whatever seems most appropriate to your situation.
All the best with your research.
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Can mirt exploratory factor analysis method be used for factor structure for marketing/management research studies because most of the studies that I have gone through are related to education test studies? My objective is to extract factors to be used in subsequent analysis (Regression/SEM) My data is comprised of questions like: Data sample for Rasch Factors Thinking about your general shopping habits, do you ever: a. Buy something online b. Watch product review videos online RESPONSE CATEGORIES: 1 Yes 2 No Data sample for graded Factors Thinking about ride-hailing services such as Uber or Lyft, do you think the following statements describe them well? a. Are less expensive than taking a taxi b. Save their users time and stress RESPONSE CATEGORIES: 1 Yes 2 No 3 Not sure
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The Mirt package generally concentrates on Item Response Theory. You can perform the Exploratory Factor Analysis you want more easily with the "fa" function in the "psych" package in R. You will also find many different and up-to-date estimation methods of factor analysis in this package.
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i’m trying to run polychotic correlation with Stata v13, but I’m confused.
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Below is a link where you should find detailed information on how to do this using a user-written command polychoric and the factormat command :
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I have adopted my questionnaire from previous literature. I want to know if I still need to carry out EFA before carrying out PLS-SEM for my thesis?
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@Zia Aslam The reference you shared here is an amazing landmark paper for the scholars doing survey-based primary data research. A must read manuscript indeed. Below is the attached manuscript in pdf.
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Hi,
I am working on exploratory factor analysis in SPSS using promax rotation.
Upon checking pattern matrix, there is one question which has factor loading greater than 1.0? should I need to ignore if loading greater than 1.0?
Also i realised there are few negative loadings in pattern matrix? Can negative loadings be still considered for the analysis?
Thanks much.
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Hello Ramya,
The pattern matrix gives the regression weights for how scores on a given variable are estimated to be formed, given some value/score on each of the respective factors. These weights can be > |1|. The structure matrix gives the simple correlation of each variable with scores on each factor, not adjusted for the relationships among factors. As such, the structure matrix should not include any values that exceed |1|.
As the pattern matrix furnishes "affiliation" values that do adjust for the relationships among factors, most folks would opt to review that first for understanding what's going on in the factor solution. However, full understanding of a factor solution requires thoughtful review of (a) the pattern and structure matrices; (b) the factor correlation matrix; (c) the variable correlation matrix; (d) variable communalities (after extraction/rotation); and of course, any relevant theory as well as understanding of measurement issues associated with the respective variables.
Negative values are also not uncommon in factor pattern matrices, just as negative regression weights may be observed in multiple linear regression. Again, recall that the purpose of the pattern matrix is to show how scores on the respective factors would be optimally weighted so as to explain differences in scores on each observed variable. Whenever you have multiple factors (and therefore a reason to rotate a factor solution in the first place), the "optimal" combination of factor scores to "explain" scores on an observed variable may have positive, negative, or both valences of estimated weights.
Good luck with your work.
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Hello everyone,
I have run a confirmatory factor analysis in R to assess the translated version of an existing questionnaire. It is unidimensional and consists of 16 adjective-based items rated on a 7-point Likert Scale.
Here are the results:
X2= 627.197, df= 104, p= 0.000, RMSEA= 0.109, CI 90%= [0.101, 0.117], SRMR= 0.063, CFI= 0.839, TLI= 0.814
I am aware of all the cutoffs; well the result of my RMSEA is troublesome. On the other hand, as I am delving into similar topics, some of tem just reported these results as satisfying and didn't conduct an Explaratory Factor Analysis.
What I am wondering is if my results are acceptable to just limit myself to report them and run no EFA study?
Or should I run EFA and then gather data again based on the model proposed by EFA results?
Thanks for your time,
Sara
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Hello all,
if you allow, I would present a different perspective. The chisquare is highly significant, meaning that the model fails in predicting the data beyond the amount expected by chance. This may be trivial or substantial, you don't know it. High sample size does not cause misfit, it increases the statistical power (which it should as it is a statistical test). The cut-off values of fit indices are complete bogus as they cannot be generalized beyond the scenarios tested in the Monte-Carlo simulations which underled the values. These were artificial and minor and do not express those fundamental misspecifications a CFA model often implies.
Hence you have to diagnose the problems and come up with a proposal.
Here's a thread in which a paper is cited that shows the process how to do it
Best,
Holger
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The items used in my study have been adapted from the instruments that have been developed by some previous researchers. Most of the recently published articles didn't show the EFA results.
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I would not feel confident adapting an instrument for which previous articles show only limited psychometric characteristics in the first place. I also concur that, depending on the size of your modifications, you should decide what to report. However, if your already have a factor structure in mind, why not choose a CFA instead?
Best
Marcel
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The Project is incomplete, Please open the file attached to see!
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Having read the project, I will recommend you use PAF, oblique rotation. The component matrix may be ignored. Use the patten matrix instead. Name the factors based on the underlying factors loading to them. Compute item means and standard deviation. Do a Cronbach reliability test for each of the factor using the items loading to them.
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I have a data which contains Three Level Items (YES-NO-NotSure). Is it technically right to transform data into numeric type and perform EFA (Exploratory Factor Analysis) to extract factor scores to use in subsequent analysis?
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There are latent variable models for categorical observed variables. Look up the nominal IRT model if you want continuous latent variables. This is implemented in mirt ( ). If you want categorical latent variables google latent class models.
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Hey guys,
I have found two multi-item scales in my previous research regarding my master thesis. I want to know if I can compute an EFA for the dependent and for the independent variable?
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Sure, to see the structure( Observed variables) for both IV and DV
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I assessed psychometric features of a construct and after exploratory factor analysis,
more than half of the items were excluded. How the construct/ content validity was influenced?
Any ideas or suggestions for reading ?
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If you change a questionnaire around you are basically going back to the development stage. Fine, your re-analysed data may achieve good statistics on the sample data that you reduced but you are simply 'modelling the data' at this stage. As a reviewer I would reject any research that relies for its conclusions on this re-analysis. What you now need to do is to gather a fresh sample on your re-constructed questionnaire and run the whole gamut of statistics on the fresh sample. You will find (perhaps to your surprise but not to the surprise of an experienced psychometrician) that those lovely values you derived from your previous, reduced and edited subset are weakened - if they hold at all.
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Dear researchers, I am a master student, and now writing my graduation thesis. I am studying how the six dimensions of post-purchase customer experience influence customer satisfaction, in turn, repurchase intention. I have adapted the measurement scales of the six dimensions of post-purchase customer experience to make it more applicable for my study context. My question is: do I have to conduct exploratory factor analysis in SPSS? I have done that, but there are so many cross-loadings, I tried different methods, but the results still look not good. There are two dimensions of post-purchase customer experience(customer support and product quality) are loading to the same new factor, I feel it is not acceptable, because they are very different. I understand there may be some problems related to my questionnaire, but I have no chance to improve the questionnaire now.
I tried to use SmartPLS to do my analysis, and the factor analysis in this software looks great,but I think the factor analysis here is CFA instead of EFA. So can I skip EFA to do CFA directly?
I will need to finish my thesis in 1 month, and I really need your help. Thank you!
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Only CFA in case you have adopted standard scale and made minor changes. But if you have constructed t he whole scale yourself as in made new items you would have to do a efa on a separate set of samples and CFA on separate set of samples
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Hello RG researchers,
I am a bit confused due to different questions and comments.
Well, I have a single factor containing 11 items (Likert rating). For the EFA, I am using SPSS (maximum likelihood) and I use lavaan and Amos for the CFA. I've got three questions:
1. KMO and Bartlett's tests' criteria are met while the normality tests (Kolmogorov-Smirnov and Shapiro-Wilk test) are not met (they are both significant). So, am I good to keep up the EFA or shall I need to use Satorra-Bentler or Yuan-Bentler adjustments (if yes, what software do I need to use)?
2. Should I be checking the normality for each item or checking the variable's normality is enough?
3. For the divergent validity, I use two other variables aside from my main questionnaire. Do they also need to be distributed normally as well?
Thanks for your time,
Sara
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1. To test normality, I recommend interpreting the skewness and kurtosis coefficients instead of statistical tests. In this case, if there are normality problems, parameter estimations can be made with unweighted least squares in SPSS.
2. Multivariate normality test is sufficient.
3. Depends on the statistic to be used. If normality is an assumption of the statistic to use, yes.
Good luck
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I am examining results from an exploratory factor analysis (using Mplus) and it seems like the two-factor solution fits the data better than the one factor solution (per the RMSEA, chi-square LRT, CFI, TLI, and WRMR). Model fit for the one factor model was, in fact, poor (e.g., RMSEA = .10, CFI = .90). In the two factor model, the two latent factors were strongly correlated (.75) and model fit was satisfactory (e.g., RMSEA = .07, CFI = .94). The scree plot, a parallel analysis, and eigenvalue > 1, however, all seem to point to the one-factor model.
I am not sure whether I should retain the one or two factor model. I'm also not sure whether I should look at other parameters/model estimates to make determine how many factors I retain. Theoretically, both models make sense. I intend to use these models to conduct an IRT (uni- or multidimensional graded response model - depending on the # of factors I retain).
Thank you in advance!
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0.70 is acceptable
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Currently, I am performing a factor analysis on 6 items.
I read that the residual plot can be used to assess the assumptions of normality, homoscedasticity, and linearity. However, I do not understand which residuals to use for this analysis. Do I need to examine 15 different plots for each combination of the 6 items?
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Why do not you apply regression method?
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Hello all,
This is my first time doing CFA AMOS.
Initially, I developed a scale for a specific industry 17 items 5 factor scale based on theory of other industries. This proposed scale was tested with two ) datasets first with n=91 year 1 and second n=119 year 2 from a single institution. EFA identified 3 underlying factors in both the datasets, no items were deleted.
During year 3, a sample of n=690 consisting of participants all over the nation was used to do CFA using SPSS AMOS. Following is the output:
1. Based on EFA (3 factors, 17 items)
a) Chisquare = 1101.449 and df= 116 [χ2/DF = 9.495]
b) GFI = 0.805
c) NFI = 0.898
d) IFI = 0.908
e) TLI = 0.892
f) CFI = 0.908
g) RMSEA =0.111 (PClose 0.000)
h) Variance
Estimate S.E. C.R. P Label
F1 .573 .056 10.223 ***
F2 .668 .043 15.453 ***
F3 .627 .040 15.620 ***
i) Covariance
Estimate S.E. C.R. P Label
F1 <--> F2 .446 .036 12.502 ***
F1 <--> F3 .365 .032 11.428 ***
2) Based on theory (5 factors, 17 items)
a) Chisquare = 440.594 and df= 109 [χ2/DF = 4.042]
b) GFI = 0.926
c) NFI = 0.959
d) IFI = 0.969
e) TLI = 0.961
f) CFI = 0.969
g) RMSEA =0.066 (PClose 0.000)
h) Variance
Estimate S.E. C.R. P Label
F1 .677 .047 14.334 ***
F2 .670 .043 15.493 ***
F3 .648 .054 12.100 ***
F4 .741 .061 12.103 ***
F5 .627 .040 15.620 ***
i) Covariance
Estimate S.E. C.R. P Label
F1 <--> F2 .503 .036 14.057 ***
F1 <--> F3 .581 .041 14.262 ***
F1 <--> F4 .546 .041 13.388 ***
F1 <--> F5 .398 .032 12.321 ***
F2 <--> F3 .457 .036 12.848 ***
F2 <--> F4 .403 .035 11.405 ***
F2 <--> F5 .458 .033 13.899 ***
F3 <--> F4 .553 .042 13.036 ***
F3 <--> F5 .360 .032 11.275 ***
F4 <--> F5 .358 .033 10.754 ***
My questions:
1. Do I have to normalize the data before CFA analysis? (I am finding conflicting information since my scale is a likert scale and extreme values are not really outliers ?)
2. Can I report that theory based model is a better fit compared to EFA model? Would doing so be appropriate?
3. Is there anything else I need to do ?
Any guidance will be greatly appreciated.
Thank you,
Sivarchana
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Hi Robert Trevethan thanks for your question.
I think ML would be suited to continuous normal data, as you suggest, and robust ML for skewed/non-normal continuous (or interval data with say 7-11 categories). So far I have only collected Likert, so because that involves polychoric correlations ML might not estimate accurately. I don't actually know if PAF in SPSS is equal or superior to, say, a DWLS in R. I think the main point I wanted to emphasise is to use PAF instead of PCA - I got this wrong in my earlier days - as PAF will be more accurate if using SPSS.
I must say Robert, your answers really make me think, which is good :) If I need to be corrected, I'm open.
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What is the best method or criteria to use in choosing the best item, when cross-loadings of items is evident in exploratory factor analysis? Thanks!
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Hello Musa,
The answer depends on your research objectives, on whether you use orthogonal or oblique rotation (assuming more than one factor, of course), and your degree of love for Thurstone's "simple structure" solution.
If you use oblique rotation, and factors have moderate to strong correlations, then you'll tend to get a lot of cross-loadings. That doesn't make the structure wrong, nor does it automatically imply that you should jettison all such variables from your solution. At the same time, this is not to say that sticking with orthogonal rotations will eliminate cross-loadings from occurring.
If you embrace the simple structure solution, then this means you want to see variable-factor loadings of near 1 (sign is irrelevant) on one factor, and near zero on all other factors. The reasons for this as a desired pattern of loadings (for some) are that it: (a) makes interpretation of salience very straightforward, (b) eliminates cross-loading acceptability debates, and (c) often makes the characterization of a factor somewhat easier.
However, if you do insist that all variables have salient loadings on one and only one factor, then you may end up excluding variables which are germane to the identification of factors. The consequence might be reduced validity for factor scores as representing the intended construct.
Good luck with your work.
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I am working on developing a new scale .On running the EFA, only one factor emerged clearly while the other two factors were messy with multiple item loadings from the different factors.
1- Is it possible that I remove the cross-loadings one by one to reach a better factor structure by re-running the analysis?
2-If multiple items still load on one factor, what criteria should I use to determine what this factor is? 
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Exploratory factor analysis (EFA) is method to explore the underlying structure of a set of observed variables, and is a crucial step in the scale development process. ... After extracting the best factor structure, we can obtain a more interpretable factor solution through factor rotation.
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Can the measured variables that remain ungrouped in exploratory factor analysis be included as separate variables during the structural equation modeling (SEM) of the latent variables observed in factor analysis? Please help me with some references.
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Thank Imran and David.
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For my research project I am adding new items to a previously validated scale. in the previous research they performed an exploratory factor analysis revealing a two-factor structure, but the internal consistency of one of the scales was quite poor so the aim of my study was to add new words to improve the internal consistency. so do i need to do another exploratory factor analysis as the scale will now have new words or can i do a confirmatory factor analysis because i'm still using the same scale?
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Robert Trevethan thank you for your reply! I will definitely have a read of those articles, but just to confirm would you recommend doing an EFA when adding new words to the scale?
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I am developing a questionnaire and first performing an exploratory factor analysis. After I have the final factor structure, I plan on regressing the factor scores on some demographic covariates. Since I am anticipating missing item responses, I am thinking of imputing the item scores before combining them into factor scores (by average or sum).
I came across a paper that suggested using mice in stata and specifying the factor scores as passive variables. I am wondering if this is the best approach since I read somewhere that says passive variables may be problematic. Or, are there any alternative solutions? Thank you!
Here is a link to the paper, and the stata codes are included in the Appendix.
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Yes... I would like to go with Alvis
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From the item under 0,32,0,40,0,50 as we have selected ? From the item that doesnt have a loading on any factor or from the items that have loading to two or three or more factors?Is there a rule in terms of the order of procedures?From which one should we start to exclude?
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First, be sure that you are running a Principal Factors (and not a Principal Components) Analysis, and that you are using an oblique rotation (correlated factors).
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From the item under 0,32,0,40,0,50 as we have selected ? From the item that doesnt have a loading on any factor or from the items that have loading to two or three or more factors?Is there a rule in terms of the order of procedures?From which one should we start to exclude?
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Tc Tülay Öztürk, essentially I agree with what Fakhar has posted. I'd add that, initially I'd proceed with caution, removing only one or a few items at a time - beginning with an item / items that don't load on any factor.
Then I might remove items that load on only one factor. That might be done in conjunction with altering the number of factors being sought.
As a result of that, items that previously cross loaded (at, say, < .20) might no longer do so, but if items persist in cross loading on two or more factors, I'd remove them.
Removal/retention of items requires care and perhaps several iterations until a satisfactory solution emerges.
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Hi everybody!
I'm performing EFA on a 400 observations database that contains 39 variables that I'm trying to group. I'm using maximum likelihood and applying a varimax rotation.
I have eliminated all the variables that have have communlaties < 0.4, I know this can be a bit "relaxed" but overall I don't have communalities that are that high (0.67 the highest one and it is only two variables), I have then dropped the variables that have a loading < 0.4 and have eliminated the variables that are cross loading (usually with loadings just above.4).
After performing all these steps, I have 3 clearly defined factors with 19 variables in total (F1: 8 variables, F2: 7 variables, F3: 4 variables). Is it acceptable to drop that many variables?
Thanks in advance!
Mauricio
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Hello Mauricio,
The question really isn't a statistical one; the answer depends on how important the 20 variables you propose to discard are to the definition and identification of the construct(s) you seek to assess.
It might be the case that a lot of variables you initially gathered or chose were either inappropriate or of poor technical quality (e.g., unreliable indicators). In such instances, discarding such variables does no harm to your ability to identify the related latent variables. There are certainly many published studies in which the "final" set of indicators retained is far smaller than the original set mustered by the researcher(s).
As a second case, if you had 39 variables which were highly related to one another, you could likely discard variables and not lose appreciable power in identification of the underlying latent variable(s). This is sometimes done when people attempt to develop "short forms" of measures that retain fewer items than the original version. The high intercorrelations pattern doesn't appear to be the case for your data set, based on your query.
If there's no relevant theory to guide you here (and the decision to run an EFA suggests that this could be at least partially the case), It might be useful to confer with domain experts who could advise as to whether the remaining variables appear to still represent a viable set of manifest indicators for the latent variables of interest. As well, other studies may exist in which like factor/s have been identified. You could compare your resultant set of variables to those which others found useful as indicators.
Good luck with your work.
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Dear Research fellows,
I hope you are well and safe.
What are the factors to identify high potential employees?
Are there any differences between these factors among different companies around the world?
I have not found so many studies using exploratory factor analysis about high potential employees in different companies.
I will be grateful if I know some about this subject matter.
Thanks in advance,
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Thank very much for the answer Peter Samuels .
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I developed my own survey based on previous themes from qualitative data. Pairs of questions were extracted from subscales from previous questionnaires in the field, and then adapted to fit the survey context. I have now completed data collection and I ran a CFA on the 'a-priori' factors and questions that were developed, and the model fit wasn't great!
I went back to the data and conducted an EFA to see what factors did work together, and the reliability, plus overall model fit when doing CFA was much, much better. The factors extracted during EFA weren't that far from the original themes, except for a couple of questions being moved around.
Therefore, my question is - is this a done thing? As this was a data-driven survey, would it be acceptable to run EFA and go by this factor structure to continue with the rest of my stats? Or should I just stick with the original 'a-priori' factor structure and deal with the consequences?
Thanks!
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Rachel--it sounds like you are really in the instrument development process here. In this case, I think it makes sense to review the EFA findings. Even if the items you selected came from several well-designed existing measures, they have likely not been presented together in a single administration, as you have laid them out. And responses to items may vary, depending on the other items to which respondents have already been exposed and the order in which the items appeared (order effects). After you revise your instrument (based on feedback from this EFA), I would suggest that you re-administer your survey in a new sample, fit your new hypothesized factor structure in a CFA framework, and examine the fit of the CFA model at that point. You may still be able to improve your scale, but also be wary of trying too hard to obtain excellent model/data fit, as doing so can exploit idiosyncrasies in a specific data set that may not translate to a subsequent sample.
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Hi all,
I've conducted an exploratory factor analysis with 365 participants, and all the data largely is reliable and has gone according to plan. However, when looking at the rotated component matrix (varimax rotation conducted), one of my questions doesn't load onto ANY factor whatsoever (no number is displayed). I've tried to find answers to this, but can't seem to find any papers that illustrate what to do when this happens. I would assume that in this case, I would discount the question altogether?
Can anyone advise on best practice, or guide me towards a paper that may answer my question?
Thanks!
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Rachel Cholerton, You are being provided with some advice up above that is well worth considering. I would make two other suggestions.
One is to use an oblique rotation (e.g., promax) rather than an orthogonal rotation (varimax in your case) because most items in an EFA are related to each other.
The other is to look very closely at any item that does not load on any factor. As has been indicated above, that item could refer to something important that does not relate strongly to other aspects of the overall construct you're measuring. If it is important, one strategy is to now create more items that you believe would be related to the "odd" item, and then obtain another set of data in which those items are included to see whether they do represent an important factor in a new EFA.
I would also look carefully at the wording of the odd item to see whether something about the way it was presented resulted in "unusual" responses. If that turned out to be the case, maybe a simple change in wording in any future research would be advantageous.
If the item turns out to be faulty or just on a different (and probably unimportant) planet, and you're not in a position to collect more data, it's probably best to simply delete it and re-run your EFA.
Incidentally, I hope you are not using the Kaiser criterion (eigenvalues greater than 1) to determine the number of factors in your data because that method often suggests there are more factors than there really are. Instead, it is better to use the scree plot or, even better, parallel analysis. In the past, parallel analysis was avoided, but software is now readily available for conducting it and it's really easy.
You'd asked for some useful references. Peter Samuels' study guide (that he recommends in his post above) is useful. I think the following might also be authoritative and informative:
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
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.
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, 511–521. https://doi.org/10.1016/j.ijnurstu.2013.10.005
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift’s electric factor analysis machine. Understanding Statistics, 2(1), 13–43.
All the best with your research.
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Hello SEM Fans,
I conducted an ESEM with target rotation using personality data. 1) Am i right that with rotation target, the calculation can only be made using listwise deletion? In this case i would pay a better model fit with lower statistical power, right? 2) Is there any possibility to simulate missing data in a way multiple imputation does? 3) In the case that ESEM is not possible because too many cases have missing data, could it be a solution to do a regular SEM with Bartlett's factor scores from SPSS instead of latent variables?
Thank you and best regards Stefan
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I can now bring some light into the dark myself:
1) normally it is no problem to deal with missing data in ESEM. You use the FIML Estimator and everything is fine. But in my case I have a binary result. This means that I have to use numerical integration (which is needed for ML). I could avoid this with Estimator = Bayes, but this is not allowed for ESEM. So I have to stay with WLSMV - but this estimator uses listwise deletion.
2) My solution is to:
first create new datasets by multiple imputation as described in example 11.5 of the User Guide and:
then calculate them with Estimator = WLSMV.
3) Answers/opinions are welcome.
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Hi everybody!
I have a market research study in which we have asked the customer to evalute the company they buy the most from on multiple attributes (30) on a scale of 1 to 10. We want to understand the different market segments that might exist based on this evaluation. We have around 300 answers.
We have no prior construct on how the different attributes might load onto different factors, so we are using EFA. My question is if we should also perform a CFA after we do the EFA. I have been doing some research about this and some people say you can run CFA on the same EFA data and some say that you shouldn't. Any opinions? Our ultimate goal is to get the factor scores for each customer and perform a segmentation using k-means.
Thanks in advance!
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Hi Mauricio,
to paint the picture a bit more colourful, I (probably) disagree with my predecessors :)
Apply a factor analytical method (EFA or CFA) IF your think and are interested in underlying common factors. I guess, your indicators are generated in a nonredundante fashion where each indicator evaluates something different, right? A factor model assumes that a) these indicators will cluster in different groups AND (more importantly) b) the reason for this clustering is in underlying response tendencies / evaluation mechanisms. By extracting or modeling such factors, you shift the level of analysis away from the precise level of each single evaluation to these more abstract and general tendencies. If this is what you want, go for it.
Further, doing an EFA and then repeating the same model in a more restrictive model (the CFA) either in the same sample or a different one, serves a lot of useful purposes but does not validate the structure and its inherent strong claims (i.e., (a) that you have identified something real, and b) that this "something" creates the specific evaluations measured by the indicators). You have to enlarge the model to do this, see
Having that said, I doubt that such bottom up processes (beginning theory-blindly with an EFA and than moving to an CFA) create a very hard way to success in which you will have to tinker a lot, replicate and improve. The reason is that by starting with indicators and moving upwards to factors and latent variables and their involved structures, you often create a messy causal structure which may be more complex than the simple structure of a factor model (in which the correlations among indicators are expected to solely stem from the underlying factors). Factor models are often unplausible from the start and in my experience, it is only realistic if you started with generating items that are designed to measure a theoretically assumed latent variable. THIS may have a chance but I doubt that factor modeling can be easily done in an exploratory fashion. In this regard, I wrote a long post in the following thread that might be infomative.
A completely different (more easy) road is conduct a principal component analysis which makes no bold claims and creates weighted sum scores of your indicators with which you can work. Yes this is more boring that you stay on the level of your measures and don't step behind but the risk to create nonsense is smaller.
Everything has benefits and costs :)
HTH
--Holger
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Research on Retail service quality and customer loyalty is being carried out presently by me.
Brief Description of the Study:
In our Scope, Retail Service Quality is considered as the independent variable. Further, it has five dimensions or Variables, Which is measured by 22 questions or items (Physical Aspects, Reliability, Personal Interaction, Problem Solving and Policy).Meanwhile, Customer Loyalty is considered as the Dependent Variable, which is measured by 8 questions or items.
Research Methodology
First of all, I intend to perform the EFA to factorize the items of independent variable (22 Questions), which will give the unique and uncorrelated factors under the independent variable.
Meanwhile, I don’t want to perform the EFA for whole 30 question or items. In which, 8 items are used to measure the dependent variable. Generally, there is a coloration or association between independent and dependent variables. Therefore, I only used 22 items under the independent variables to perform the EFA to construct the unique model.
Secondly, I wish to perform the CFA with the identified items of the factors under the independent variable via EFA and items of dependent variable, those are not factorized via EFA ( 8 items) to confirm the whole set of model , which contains both independent and dependent variable under the measurement model.
Thereafter, I also like to perform the Structural Equation Model (SEM) to find out the path way between independent variables (Physical Aspects, Reliability, Personal Interaction, Problem Solving and Policy) and dependent variable as Customer Loyalty.
Sampling Adequacy
What is the required level of Sample size for the advance statistical tools as Exploratory Factor Analysis and Structural Equation Model?
Whether Two thousand (2000) sample size is enough or too much or less to get the significant model
If it is too much, how we will tackle it smoothly to get the Significant Model.
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it is correct-- u can analyse the brand switching and brand sticking factors the influence customers
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I need a confirmation regarding Exploratory Factor Analysis (EFA). from literatures that I have already read, we must include all variables and items we had in the research model to run EFA.
When a new research model was developed by combining 2 established theory, is there any possibility and justification for me to run EFA on theory A first, and then EFA on theory B?, or i can separate EFA based on Independent and Dependent Variables?
Please advices...
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I think, if you can manage to do a further study after that, then you could do a step-wise approach in which you begin with a smaller model and then build it up.
As I said, things will probably change when you add other variables. I often found a nicely fitting small CFA model but when I added another construct with its set of indicators everything exploded.
When you do just one study (with no extra validation) and you rest your "validity evidence" on doing a small EFA with 4 indicators, then this is weak evidence. As a reviewer, I would strongly criticize that.
Best,
--Holger
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Hi,
I am running an Exploratory Factor Analysis (EFA) on SPSS and trying different extraction methods. The Principal Component Analysis (PCA) suggested 4 factors whose Eigenvalue (EV>1). The Parallel Analysis suggested that factor 4 be dropped. This is also consistent with the Scree plot output.
When trying the same procedure using Principal Axis Factoring (PAF), I immediately get 3 factors with EV>1. However, when I try to ascertain that result in the Parallel Analysis, all EV I get are lower than 1.
While I intend to proceed with a 3-factor solution as suggested by PCA, I am nevertheless curious to know what does the Parallel Analysis (EV<1) result suggests about the extraction method. Thank you for your kind suggestions.
Regards,
Kimo
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H. Kimo Boukamba, I'm not exactly sure what's going wrong for you, but it seems you're not conducting parallel analysis correctly. Perhaps try the following site:
In it, enter your information (number of items and number of participants) and I think you can retain the default entries for the other fields.
Can you try that and see whether you get better results?
Incidentally, "officially" PCA isn't really EFA, even though you'll probably get similar results either way.
I think that, if your scree plot and parallel analyses indicate there are only 3 factors in your data, I'd run with that. Using eigenvalues > 1 (the Kaiser criterion) is often not a good strategy for determining number of factors. In fact, I have often found it quite misleading.
Do feel free to get back if you keep having problems.
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I am working on validating Multi-Dimensional scale, total variables are 8 with total 56 items, how much sample size is required to run Exploratory factor analysis?
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Dear Waqar Ahmed Sethar The are multiple approaches to estimate the minimum sample size. However, the number of factor sololy is not enough to answer this question. These techniques differs in their complexity. Relying on either 1. Rule of thumb 2. Power Analysis 2. Monte Carlo Simulation And I would recommend you to take a look into this paper that may give you the guidance to fulfill your sample size requirements sufficiently. Here is the paper link: https://www.researchgate.net/publication/327180990_Applied_Psychometrics_Sample_Size_and_Sample_Power_Considerations_in_Factor_Analysis_EFA_CFA_and_SEM_in_General Here is the citation: Kyriazos, T. (2018) Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General. Psychology, 9, 2207-2230. doi: 10.4236/psych.2018.98126.
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There's two types of Factor Analysis as we know, that is Confirmatory Factor Analysis(CFA) and Exploratory Factor Analysis(EFA). Do you know any other kind of it?
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Hamid Reza Farhang Thanks for the link. Thanks so much.
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Hello researchers,
I have a four-factor model determined a priori (some emergent theory) to which my data fits quite well when I do confirmatory factor analysis (CFI>0.98; TLI>0.98; RMSEA<0.03; SRMR<0.04; BIC-sample adjusted = 8107)
When I first perform exploratory factor analysis on the data I arrive at a two-factor model which combines the items in the four-factor model such that factor 1&2 in the four-factor model (with over 85% covariance) load highly on the first factor of the two-factor model and factor 3&4 (with over 85% covariance) in the four-factor model load highly on the second of the two factor-model. On conducting another CFA, the data fits quite well with the two-factor model from the EFA (CFI>0.97; TLI>0.97; RMSEA<0.03; SRMR<0.04; BIC-sample adjusted = 8117 )
The 2-factor structure seems simpler in terms of number the factors but has slightly lower fit statistics. (Q1) How do I interpret these differences in the two structures? ie. What can go wrong with the interpretation if I am to rank and prioritize items by the regression weights on respective factors using the two-factor structure rather than the original 4 factor-structure? (Q2) Which model comparison tests (or theoretical argument) can I use to ascertain which is the best of the two models for explaining the underlying structure of the phenomenon.
Any thoughts?
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The two-factor model involves a single correlation between those factors, while the four-factor model involves either 6 correlations if you allow for the full set or 3 if you group them with second-order correlations. That means you can test the difference between the two-factor model and four-factor models with either 5 degrees of freedom or 2.
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I am currently trying to create a scale to measure a multi-dimensional parenting construct. There is currently no strongly established theory about the construct and I am investigating it in an age group that has not typically been the focus of parenting researchers. I created a list of 26 items based on a qualitative study and have done an EFA on the data. Almost half of the items are skewed and some are quite kurtotic due to low base rates of those parenting behaviours. However, I believe that these items are theoretically relevant to the construct of interest. Due to high skew/kurtosis/presence of non-normality, I used polychoric correlations for the EFA. A 3 factor solution was recommended.
My questions are:
1) The determinant of the matrix is less than .00001 but Bartlett's and KMO are good (fit indices are generally good as well). I have read in previous discussions online that <.00001 determinants may arise due to high kurtosis in items. Does anyone know of a reference/resource that explains this in more detail and/or has recommendations that it's not the end of the world?
2) A number of the skewed/kurtotic items have low communalities (<.40) even though they have factor loadings of over >.40. What are the best practices or existing rules of thumb on how to proceed with elimination of items to refine the scale? Should I delete the items with low communalities (despite the sufficient factor loadings), and then re-run EFA? Or should I delete items based on low factor loadings (<.40), then re-run EFA? If the latter, would it be necessary to do anything with (i.e., elimiate) the items that have low communality? Or just leave them?
Thanks very much in advance.
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Vivien So... One of the very important aspects of scale development is the sample size. You need to have to adequate sample size to perform EFA analysis, otherwise, problems like skewness and kurtosis will appear. Further, in your study (as it is exploratory in nature), you can initially retain items with low commonalities (<.40), but check whether items these are cross-loaded on some other factors. If so, delete them. These are the following articles that you may find useful:
  • Boateng, G. O., Neilands, T. B., Frongillo, E. A., Melgar-Quiñonez, H. R., & Young, S. L. (2018). Best practices for developing and validating scales for health, social, and behavioral research: a primer. Frontiers in Public Health, 6, 149.
  • Hinkin, T. R. (1995). A review of scale development practices in the study of organizations. Journal of Management, 21(5), 967-988.
  • Morgado, F. F., Meireles, J. F., Neves, C. M., Amaral, A., & Ferreira, M. E. (2017). Scale development: ten main limitations and recommendations to improve future research practices. Psicologia: Reflexão e Crítica, 30 (1), 1-20.
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Hello.
I conducted a pilot survey (n=67). I modified the survey based on respondent feedback and a principal component analysis, and I administered it to a larger sample (n=561). I ran an exploratory factor analysis with the new data omitting the demographics variables. I obtained three factors that work out nicely. The first two factors yielded an acceptable Cronbach's Alpha coefficient (.784 and .772, respectively), but the third factor has a coefficient of .485. One of my research question was whether factor 3 affected factor 1, and the factor correlation matrix shows a correlation coefficient of 0.488.
My questions are:
1) Is it okay to omit demographic variables in an exploratory factor analysis? I am not testing demographics as a construct, I want to find the correlations between the different demographics (e.g., type of math, grade level, school location) and the factors.
2) Do I conduct further statistical analysis (i.e., frequency and correlation) on the first two factors only since those have acceptable Cronbach's Alpha but the third one does not?
3) I heard that any correlation of 0.32 and above is considered acceptable between factors. Is that true? If that is case, should I say that factors 1 and 3 have a strong correlation but then indicate that the low internal reliability for factor 3 does not allow us to generalize results to the general population?
4) In general, if we ever eliminate any variables in an EFA, do we completely ignore those variables in further statistical analysis?
I'm sorry for so many questions. I have found a lot of information about how to conduct an EFA, but not what to do with and after the results.
Thank you in advance for your help.
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Veronica Bass, thanks for providing some reassuring feedback. I'm aware that some of your original questions have not been answered by either Jimmy Zhong or me. However, it seems you've already "answered" them yourself, so pls feel free to get back with any residual concerns or uncertainties you might have.
Incidentally, "officially" it's coefficient alpha, not Cronbach's alpha. Even Lee Cronbach himself indicated that the index should not carry his name. :-)
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Many researches have Exploratory Factor Analysis followed by Confirmatory factor Analysis when theory is available. My research has not established model can I apply this Exploratory Factor Analysis and the result cab be taken as a scale developed
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Generally speaking, the EFA does not have to be followed by CFA, since the two analysis seeks different targets. EFA is mainly used for scale reduction and CFA is mainly used when the aim is to validate a measurement model in the structural equation context.
Now regarding the part that there is no theory available and that your research has not a proposed research model yet. However, I would expect that your questionnaire has a set of pre-defined (factors/constructs) that the (items/questions) are trying to measure.
Therefore, If you are developing a new scale then you definitely should apply EFA and ensure that the new (items/questions) are properly loaded on the targeted (factors/constructs). Later, once your new scale validated with EFA of identified (factors/constructs), you can run CFA, to validate the measurement model.
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Factor analysis classified into two. That is obviously Exploratory and confirmatory factor analysis. So I need a clear explanation a bout the difference between the two?
Thank you in Advance!!!
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Thank you so much!!!
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i design a questionnaire about job health . data collection and exploratory factor analysis was done. can h used the responses of participant to report job health of the sample.
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EFA is an assessment of measure validity and using the sample in further analyses depends on the nature of your research. Our recent article provides deeper insights into this and proposes a paradigm regarding measures development.
Best,
Ali
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I have seven latent variables but in exploratory factor analysis only six factors came and some questions falls under different factors. My query is while performing CFA model those questions falling under factors are considered or as per my questionnaire seven latent variables are to be considered ignoring EFA.
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When you efa shows six factors i guess you should go with it into cfa and the same way for path analysis .In case you want to take seven you will have to ignore efa.But then you must have done efa as the scales were new or adapted in whcih case efa is crucial so you should consider its resluts too.Also it is absolutely fine if the factors get loaded in six not seven factors ...this could be a new finding for my target sample and something nonone has done before.The vals model had eight factors,researchers of japan have devised a new vals for themselves as the efa or cluster analysis did not show the same eight factors in their country
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Graduate research (Ph.D.) students very often face the dilemma of whether to use EFA along with CFA (or CCA) while conducting measurement model analysis in SEM in basic business research with perception-based latent variables. Finally, there comes an article (reference given below) that discusses in detail about these construct measurement concepts from PLS-SEM and CB-SEM perspectives.
Hair, J. F., Howard, M. C., & Nitzl, C. (2020). Assessing measurement model quality in pls-sem using confirmatory composite analysis. Journal of Business Research, 109, 101-110. doi:10.1016/j.jbusres.2019.11.069
I hope this well-written paper would now serve as a primary reference for all those who seek emancipation from the never-ending (long-created) confusion about the use of EFA/CFA/CCA while conducting measurement model analysis, especially in SEM (PLS-SEM and CB-SEM).
I hope respected business research scholars would enlighten further our thought on the matter by providing their insights on the topic.
Best regards.
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Dear all,
please see the following article who compares CCA as originally developed and the measurement evaluation step knwon from PLS-SEM:
Best regards,
Florian
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What can be the advantages of performing EFA prior to CFA, when we are building an instrument against a pre-defined conceptual framework?
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In my experience, if you've theoretical backing for a model including 26 latent factors, and corresponding items are adopted from already published scales/instruments, you should go for CFA. However, as mentioned by Robert and David, you will need to big sample size to run CFA for 26 variables altogether.
Further, since you mentioned SEM and the AMOS, I believe you are talking of SmartPLS SEM in former case. This also, kind of, points that you don't have a big sample size either ( pure assumption based on your query). So, if sample size is not that big, I would recommend dividing the model into smaller model (of course supported by theory). Handling 26 latent variables in AMOS will be challenging, not because AMOS cannot handle it but because of poor GUI of AMOS. I will definitely go SmartPLS SEM with as many variables as yours.
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In Factory Analysis perspective, What is the difference between exploratory factor analysis and confirmatory factor analysis? What will be the ideal sample size to analysis EFA and CFA?
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The easiest way to see the difference is: in CFA you already have the answer you just looking to provide either evidence to support it or evidence to disprove it, whereas in EFA you are like a detective on the path of finding the answers by gathering the data and then looking for your answer in that data. In terms lf sample size, for both type of analysis you need fairly large samples. I would reccomened somewhere between 350-500 minimum.
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I have reviewed many articles about the pilot study, in some, they run the reliability test, while in other along with the reliability they run the EFA. I would like to know is it necessary to run EFA along with reliability test ? in case we already adapted the item from literature and content validity is conducted by calculating content validity index (CVI)? (Note that my sample size is less than 50).
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Reliability is the first thing you chcek.with cronbach alpha.Then in case toy havent taken standard scales from authors do a efa.One factor loadings are ok you do a cfa.Also efa and cfa are not done on the same sample
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  • Most of us are using adapted scales while conducting research, but there is confusion on the application of exploratory factor analysis (EFA) on such scales. If the constructs are already identified in the questionnaire then should we apply EFA on the full scale or it should be applied on each construct?
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Helle Prachi
this question is among the most asked questions on RG. See for instance,
Short form: Whenever you have an idea about a model, specify your idea and test it. Then adapt when necessary.
Best,
--Holger
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Hi,
I conducted a principal axis factoring (PAF) with oblimin rotation on a scale with 5 items. 2 factors were extracted (using Kaiser's criteria (eigenvalue >1) and scree plot analysis): 2 items load on factor 1 (F1) and 3 items on factor 2 (F2). Items do not cross-load.
All items are measuring the feeling of efficacy but different dimensions of it. F1 seemingly measures self-efficacy (my family & friends (item 1), and I (item 2) can do something to...). F2 describes collective efficacy (people in general (item 3), businesses (item 4), governments (item 5) can do something to...).
If I force PAF to extract only 1 factor (to measure "general" efficacy), all item factor loadings are still >.5, and Cronbach's alpha of the 5-item scale is above >.7.
However, I am not sure what would be the better way to proceed to build a regression model with "efficacy" as one/or two independent variable/s: Go for the 1-scale solution (to avoid a 2-item scale of "self-efficacy") and simply mention that efficacy has two dimensions that are measured together in one variable? Or split efficacy into two scales? I saw both approaches in research.
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You can look at our paper:
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Hi,
I have performed factor analysis in order to categorize 31 variables into major groups, the result yielded 9 factors however, in the rotated component matrix I have found two factors with only one attribute (one variable) but with a high loading value. Is it normal to take a factor with one variable or I have to delete this factor??
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Hello Roumeissa Salhi,
Having high loading on the factor is good, especially if the scale is being designed for individual diagnostic (DeVellis, 2003; Nunnally, 1978). However, factors with less than three items are considered “weak and unstable” (Costello & Osborne, 2005, p. 4), and would necessitate ignoring the factor in further analysis, in accordance with Velicer’s and Fava’s (1998) posture that factors with less than three variables with high loadings should not be interpreted.
Blessings,
Hazel Traüffer
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Hi,
I want to construct an index 'X' (like 'wealth-index'/'gender development index') with 3 hierarchical scores (low-medium-high) for Bangladesh. I have found a literature where they have initially included 8 factors which are generally considered as validate domains of 'X' in Bangladesh. Then, after EFA and CFA, they have excluded 3 factors and declared that the remaining 5 factors are the 'valid factors' of 'X'. I will use 'DHS' data, like they've used too.
Now, my question is,
"If I want to create an index of 'X' (and further logistic regression) for Bangladesh with low-medium-high scores, then with proper citation of that literature, can I use those 5 valid factors/variables directly in my study (without further CFA analysis)?"
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If you want to link among them then go for CFA or just to find out the factors then EFA is easier for you.
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I am writing a paper assessing unidimensionality of multiple-choice mathematics test items. The scoring of the test was based on right or wrong answers which imply that the set of data are in nominal scale. Some earlier research studies that have consulted used exploratory factor analysis, but with the little experience in data management, I think factor analysis may not work. This unidimensionality is one of the assumptions of dichotomously scored items in IRT. Please sirs/mas, I need professional guidance, if possible the software and the manual.