I have interviewed 360 people. My questionnaire is having 40 items. I have used six latent variables. these 40 item are under these 6 latent variables. Each items are having different options. It is not an scaling questionnaire. But each item have few options. some items are having 7 options and few are three. with this data I want to know the relationship among latent variable along with the items I have used. I have theoretical support for all the latent variable with the other variables. With this kind of data can I run confirmatory factor analysis by SEM ? If not CFA how can I find the correlation among them ? Can someone kindly help me. I t would be a great help.
Hi Pratapa
So you have a set of indicators that use response formats with different numbers of categories? This shouldn't too much of a problem. Many latent variable modelling packages will be able to compute an appropriate correlation matrix, but this matrix will have different types of correlations. First, you'll have to decide which indicators, if any, you think can be treated as continuous. In this case, for example, I might proceed on the basis that the scores on the 7-category items are continuous and the 3-category items are ordered categorical. For the 7-category items Pearson product moment correlations will be computed, for the 3-category items polychoric correlations will be computed, and correlations between the 3- and 7-category items will be polyserial correlations.
Once this matrix is computed it looks just like a regular correlation matrix. However, when estimating a CFA model based on such correlations then it's necessary to use an appropriate estimator such as weight least squares (mean variance adjusted). All this can be done quite easily in Mplus, lavaan, and other SEM software.
Mark
If using CTT (factor analyses), your options are limited to binning / regrouping response options. If using IRT, you can include items with differnce response options.
Hope this helps,
Matt
Hi Pratapa,
Yes, you are in the right track on Covariance-based type SEM. I couldn't stress on how important it is to have sound priori theory before proceeding this. Mark Shevlin has pretty much sum up what you need to do next. Continue to check for multivariate normal distribution assumption as well multicollinearity check before running your structural model. Bear in mind, some of the indices for CB-SEM is quite difficult to achieve and rather than forcing your data to comply to them, you do have other option such as variance-based SEM, i.e., PLS SEM to consider. Hope this helps.
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