MANCOVA - some assumptions not met. Where next?

Hello Jack Arnold

. After reading your post, I have some questions.

1) Do you have one multivariate research question, or do you have 3 univariate research questions? That question is prompted by comments in the classic article by Huberty & Morris (1989). If you have never read it, please do before proceeding. See also the great article by Francis Huang (second link below).

Article Multivariate Analysis Versus Multiple Univariate Analyses

Article MANOVA: A Procedure Whose Time Has Passed?

2) (M)ANOVA and (M)ANCOVA models as classically defined omit the covariate x group interaction from the model. This constrains the regression lines to be parallel. If scatter-plots suggest it is unwise to impose that constraint, you can include the covariate x group interaction. Whether you could still call the model (M)ANOVA or (M)ANCOVA depends on the convention in your discipline. (In some disciplines, those names are strictly reserved for models that omit the covariate x group interaction.)

I hope this helps.

Ma'Mon Abu Hammad

For my doctoral thesis, I am looking to control for a covariate using a MANCOVA. I have three groups (Hoarding Disorder, OCD, and Control), and I have three DV's (all continuous). I've explored whether the data meets the assumptions required to use a MANCOVA, and there are two sticking points. 1: The data for some of the DV's is non-normal, and 2: The assumption of heterogeneity of regression slopes is not met. I understand that the non-normality of the data is not such a big problem as the MANCOVA is robust enough for this violation, but I have read that because of the latter, I am unable to continue with a MANCOVA. I have tried to look for alternative methods, but so far have had no luck. I'm wondering if there were any options to explore group differences for the three DVs, whilst controlling for a covariate (OCD score). I'm not sure if this is enough information, and if so, please let me know and I can share whatever you need.

ChatGPT

It's great that you're being thorough in assessing the assumptions and potential challenges in your analysis. Given the specific issues you've mentioned regarding the non-normality of some DVs and violation of the assumption of heterogeneity of regression slopes, there are alternative approaches you can consider to analyze group differences while controlling for a covariate (OCD score). Here are a couple of options:

Robust MANCOVA: While the assumption of normality is important in classical MANCOVA, you're correct that MANCOVA is generally considered robust to moderate deviations from normality, especially if your sample size is reasonably large. However, the assumption of homogeneity of regression slopes is more critical. If you believe that the heterogeneity of regression slopes assumption is not met, you might consider using robust methods for MANCOVA. Robust methods are designed to handle violations of assumptions more gracefully. Robust MANCOVA can be performed using specialized software or statistical packages that offer robust methods. These methods can provide more accurate results when assumptions are not met.

ANCOVA or Regression with Interaction Terms:If the assumption of heterogeneity of regression slopes is a concern, you might explore using ANCOVA (Analysis of Covariance) or regression models with interaction terms. In this approach, you can conduct separate regression analyses for each DV, including the covariate (OCD score) and the group variable as predictor(s). To account for the group differences while controlling for the covariate, you can include interaction terms between the covariate and the group variable. This approach allows you to model potential differences in the effect of the covariate across different groups.

Non-Parametric Methods:If you're still encountering challenges with the assumptions and robust methods are not suitable, you might consider non-parametric alternatives. Non-parametric tests, like the Kruskal-Wallis test (a non-parametric alternative to ANOVA) or the Mann-Whitney U test (for pairwise comparisons), can be used to assess group differences without making strong assumptions about the data distribution. For controlling for the covariate, you can perform rank-based versions of ANCOVA or regression, such as the Jonckheere-Terpstra test.

Bootstrapping:Bootstrapping is a resampling technique that can be useful when assumptions are not met. It involves creating multiple resamples of your data and calculating statistics of interest on these resamples. Bootstrapping can be applied to MANCOVA or ANCOVA to obtain more accurate estimates of p-values and confidence intervals when assumptions are violated.

Remember, the choice of method should align with the goals of your analysis and the specific characteristics of your data. Consulting with a statistical advisor or an expert in your field who can examine your data and research design in detail is highly recommended. They can provide personalized guidance on the best approach to address the challenges you're facing while still meeting the goals of your doctoral thesis.

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