Dear all,
I am currently exploring Latent Profile Analysis (LPA) and have noticed a trend in some of the papers I've read. After completing LPA to categorize subjects into groups, these studies often proceed directly to further analyses such as ANOVA, without conducting tests for normality or homogeneity of variance. I am curious if this approach is considered methodologically sound.
For context, in my own research, I have divided participants into three groups and performed the Shapiro-Wilk test, which indicated that none of the groups conform to a normal distribution. Despite this, I am interested in conducting an analysis of differences between groups. Consequently, I opted for the Kruskal-Wallis test. Is this approach justified in this context?
I appreciate any insights or advice on this matter.
It makes sense to use the Kruskal-Wallis test in your research, especially in regard to the Shapiro-Wilk test results which show your data are not normal. While some studies frequently neglect to validate assumptions such as normality and homogeneity of variances before to ANOVA, best practice is to do so, especially in rigorous statistical analysis. When these assumptions are not satisfied, as they are in your situation, the Kruskal-Wallis test-a non-parametric substitute for ANOVA-is appropriate.
You could do it in this way, but the "classify-then-analyze" approach to examining covariates of class membership in LCA and LPA is considered suboptimal by many because it re-introduces measurement error. When you classify individuals according to their most likely latent class membership, there will typically be many (most?) individuals for whom their most likely class probability is < 1.0 (and sometimes substantially below 1.0). Therefore, when you classify people, you re-introduce uncertainty--something that we are trying to minimize by using latent variables.
A better approach is to include your covariates of class membership directly into the model and to examine differences between classes without first classifying individuals according to their most likely class membership. This also provides greater statistical power and avoids a multi-step process.
Related to Christian Geiser 's point, many of the statistics that you might apply (e.g., t-test) assume the groups have no measurement error. The structural after measurement approaches address this. That said, this assumption is often ignored. I would go with Christian's suggestion. How high are the probabilities? And do the classes make sense?
Yes, it is appropriate to conduct ANOVA analysis directly after Latent Profile Analysis (LPA)
ANOVA is an essential tool that can be used to validate the LPA solution by evaluating between-group differences on clinical, functional, and HRQoL outcomes.
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