I've applied a survey with approximately 200 innovative companies, using widely validated by previous studies innovation capabilities measurement instrument, likert-scale from 1 to 5
As the capabilities of the companies (all of the involved in University-Industry Cooperation) showed very high results, most values are concentrated on 4 and 5, so, skewness is really high. Smirnov-Kolmorov showed non-normal distribution for almost all variables (spreadsheet attached)
Sample have almost no outliers. And the thing is it was not possible to foresee ex-ante that firm's capabilites would be so high.
My data analysis technique will be QCA, however, I would like to perform first the CFA first.
Please, help me! Thank all of you in advance!
Andrei Mikhailov You can use WLSMV estimation with polychoric correlations in Mplus to analyze ordinal items in CFA (see https://www.statmodel.com/usersguide/chapter5.shtml). In lavaan (R package), this procedure is referred to as DWLS (see https://lavaan.ugent.be/tutorial/cat.html).
References
Article On the Performance of Maximum Likelihood Versus Means and Va...
https://www.proquest.com/openview/2d3fd14395e98d066cadb5ff016fab85/1?pq-origsite=gscholar&cbl=18750
Article Analysing multitrait-multimethod data with structural equati...
Hi,
DWLS expects a normally distributed latent response variable underlying the ordinal response. And as simulations studies show that likert scales with >= 5 categories work fine I would rather use robust ML (that is by applying the Satorra-Bentler or Yuan-Bentler corrected versions of the chisquare test and robust standard errors. Here are some papers of which esp. Li (2016) may be highly relevant. He shows that DWLS is better in estimating loadings but weaker in estimating factor correlations. However, I would assume that your severe nonnormality would make the case for robust ML even more salient :)
All the best,
Holger
Li, C.-H. (2016). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936-949. doi:10.3758/s13428-015-0619-7
Rhemtulla, M., Brosseau-Liard, P., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373.
Chou, C.-P., Bentler, P. M., & Satorra, A. (1991). Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: A monte-carlo-study. British Journal of Mathematical and Statistical Psychology, 44, 347-357.
Enders, C. K. (2001). The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data. Psychological Methods, 6(4), 352-370.
I agree with my colleagues,
WLSMV estimator is also possible to use in Lavaan as well. It helps, but sometimes does not "save". If you may use a "simple mean" to compose the factor and not the loadings of the items, you are looking only for the structure and good fit, but you still have a factor problem. I don't know if I made my point.
It is possible to conduct parallel analysis for polychoric factors (using Psych), and conduct omegas instead of alphas. But again, I applied it before because I had a similar problem, and the difference in structure was zero, the loadings differ, are really better, the omega as well. Still, the factor structure, in practical terms, was the same.
Thus, I used parallel analysis and omegas and composed the factor using loadings weighted average and compare.
I hope it helps.
Regards,
Amalia
Hi Lucky,
I never test for normality because it's futile. Tests of multi-normality even more. Rather take a look at the severity and to be safe use an robust estimator (or robust calculation of the SE).
HTH
Holger
L. Sibanda I think it is good practice to carefully examine the univariate distribution of all variables in your analysis/model to get a sense for the data. I think that for that purpose, graphical methods (e.g., histograms, boxplots) and descriptive measures (e.g., skewness, kurtosis) tend to be more useful than tests of significance. Tests of significance are heavily dependent on sample size, and the null hypothesis of a perfect normal distribution may not be realistic in the first place for many variables in the social/behavioral sciences.
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