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  1. Does a latent variable in SEM need to be defined by validated scale or can you "imagine" one? For instance, I work on school participation (defined in research by attendance to school and invovlment in school activities). I have several measures: 1/ school attendance of the child (which can be 0%, < 50 %, > or = to 50 % and 100 %); 2/ activities attendance (defined by 5 activities and I know which activity the child is doing on not. So I can have a score from 0 to 5); 3/ involvment in the activities performed (for each activity, I know if the child is poorly to highly involved (5 points scale), so I can have a mean activity involvment. I Suppose that this 3 measures correspond to the latent variable "school participation". Can I run a CFA, even if there is no previous study using these specific measures for this latent variables?

  2. if the answer is yes to the question 1, is it a problem if the scales are not the same for each measure? I think the first measure is a problem as it is categorical, but I could turn it to ordinal (0 = no school to 3 = full time school). Am I allowed to do that? Is it better? If yes, is it ok for running the CFA if this measure is from 0 to 3, the second one is from 0 to 5 and the last one from 1 to 5?

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  1. Yes, you can run a CFA. Often, the purpose of CFA is to test the validity of a new multi-item/multi-component measure, so there is nothing wrong with testing such a "newly defined" latent variable model. It can help you find out, for example, whether these indicators load highly on a single latent variable. Notice that a CFA model with a single factor, three indicators, and different loadings is just identified (saturated). It cannot be tested by chi-square unless there are additional variables in the model. But it can still be used to estimate the factor loadings and indicator reliabilities (R-squared values).

  2. It is not a problem that the items are on different scales. You can analyze binary, ordinal, and/or continuous variable indicators in the same model/on the same factor. You should make sure that you select an appropriate estimation method for categorical (non-continuous) indicators (e.g., DWLS/WLSMV for binary/ordinal indicators)

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