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Thread: Multivariate and univariate outliers

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    Multivariate and univariate outliers


    Can I just check my understanding of something?! In order to run a repeated measures ANOVA, perform mediation analysis using structural equation modelling and carry out hierarchical linear multiple regression analysis, all three tests have the assumption of no outliers.

    I'm aware that there is a distinction between univariate outliers and multivariate outliers. Do all three tests essentially require that the data is free of both?

    From my reading, it seems that multivariate outliers are assessed using mahalanobis, cooks distance and leverage values, and univariate outliers are assessed looking at z scores (+/- 3). is this correct?

    Also do all three tests assume univariate (e.g. tested through skew/kurtosis, shapiro-wilks etc.) and multivariate normality (tested through mardia's coefficient)?

    Many thanks in advance,

    Last edited by EmmaL; 05-04-2017 at 12:21 PM.

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    Re: Multivariate and univariate outliers

    I don't know the test you reference (performing mediation analysis using structural equation modeling sounding incredibly complex for a test) but in a regression I suspect they are most interested in multivariate outliers. I don't think you assess outliers with Cooks distance, you assess leverage which is a different concept (the concept of outliers is part of leverage, but you can be an outlier and not have high leverage). When I generated multivariate outliers I did use mahalanobis distance - I think this is recommended.

    Univariate outliers are found many ways. Standardized or better studentized residuals are commonly a way to look for them in linear regression (I don't think this works with all forms of regression, but if you are doing ANOVA you are assuming linearity). This is not the same thing as a z score.

    I think you need to find the exact names of the test to really answer this question.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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