Exploratory Factor Analysis - Science method

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.

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.

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.

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.

Shikha Ahuja

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.

Christian and Ali, thanks for your posts. Appreciated. I'll follow up on both of them.

Robert

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:

The issue is not my specialty , with my best wishes

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.

Take a look at the attached Google search for your answer. Best wishes, David Booth

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.

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.

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.

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.

VALUES SHOULD BE GREATER THAN .05

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.

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).

Hi Sultana Razia

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

Amalia Raquel Pérez Nebra

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?

Dear Jung Eun Kim

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

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!

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.

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.

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 :

(https://stats.idre.ucla.edu/stata/faq/how-can-i-perform-a-factor-analysis-with-categorical-or-categorical-and-continuous-variables/)

@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.

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.

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

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

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.

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.

Sure, to see the structure( Observed variables) for both IV and DV

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.

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

Hi Sara Hoseingholizade

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

0.70 is acceptable

Why do not you apply regression method?

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.

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.

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.

Thank Imran and David.

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?

Yes... I would like to go with Alvis

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).

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.

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.

Thank very much for the answer Peter Samuels .

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.

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.

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.

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

https://www.researchgate.net/post/Can_we_do_exploratory_and_confirmatory_factor_analysis_in_the_same_data_set2#view=5486170ad4c118047c8b477f

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.

https://www.researchgate.net/post/How_to_deal_with_Single_and_Multiple_Item_latent_variables_in_Structural_Equation_Modeling#view=5e849fe521137522f2332355

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

it is correct-- u can analyse the brand switching and brand sticking factors the influence customers

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

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:

https://analytics.gonzaga.edu/parallelengine/

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.

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.

Hamid Reza Farhang Thanks for the link. Thanks so much.

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.

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:

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. :-)

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.

Thank you so much!!!

Hi Fariba Jowkar

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

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

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.

Helle Prachi

this question is among the most asked questions on RG. See for instance,

https://www.researchgate.net/post/EFA_exploratory_factor_analysis_CFA_confirmatory_factor_analysis_or_both#view=5c9937470f95f1a905604215

Short form: Whenever you have an idea about a model, specify your idea and test it. Then adapt when necessary.

Best,

--Holger

You can look at our paper:

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

If you want to link among them then go for CFA or just to find out the factors then EFA is easier for you.

Jimoh Mohammed Idris - See examples below.