# Repeated Measures and MANOVA

Analysis of variance, repeated measures modeling, and multiple comparisons for data with multiple responses

Repeated measures models are regression models in which observations have multiple response variables. Multiple analysis of variance (MANOVA) is a statistical technique used to determine whether vectors of response data are statistically different. Repeated measures models and MANOVA are commonly used in crossover and longitudinal studies and the response variables typically correspond to measurements taken at different times. Statistics and Machine Learning Toolbox™ provides functions for working with repeated measures models including functions for performing one-way, two-way, and N-way multiple analysis of variance (MANOVA); analysis of variance (ANOVA); analysis of covariance (ANCOVA); and for creating `RepeatedMeasures` model objects.

## Functions

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#### Create `RepeatedMeasures` Object

 `fitrm` Fit repeated measures model

#### Work with `RepeatedMeasures` Object

 `ranova` Analysis of variance for within-subject effects in a repeated measures model `anova` Analysis of variance for between-subject effects in a repeated measures model `mauchly` Mauchly’s test for sphericity `epsilon` Epsilon adjustment for repeated measures anova `multcompare` Multiple comparison of estimated marginal means `manova` Multivariate analysis of variance `coeftest` Linear hypothesis test on coefficients of repeated measures model `grpstats` Compute descriptive statistics of repeated measures data by group `margmean` Estimate marginal means `plot` Plot data with optional grouping `plotprofile` Plot expected marginal means with optional grouping `predict` Compute predicted values given predictor values `random` Generate new random response values given predictor values

#### Create `manova` Object

 `manova` Multivariate analysis of variance (MANOVA) results (Since R2023b)

#### Work with `manova` Object

 `barttest` Bartlett's test for multivariate analysis of variance (MANOVA) (Since R2023b) `boxchart` Box chart (box plot) for multivariate analysis of variance (MANOVA) (Since R2023b) `canonvars` Canonical variables (Since R2023b) `coeftest` Linear hypothesis test on MANOVA model coefficients (Since R2023b) `groupmeans` Mean response estimates for multivariate analysis of variance (MANOVA) (Since R2023b) `multcompare` Multiple comparison of marginal means for multiple analysis of variance (MANOVA) (Since R2023b) `plotprofile` Plot MANOVA response variable means with grouping (Since R2023b) `stats` Multivariate analysis of variance (MANOVA) table (Since R2023b)
 `manova1` One-way multivariate analysis of variance (MANOVA) `manovacluster` Dendrogram of group mean clusters following MANOVA

## Objects

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 `RepeatedMeasuresModel` Repeated measures model object
 `manova` Multivariate analysis of variance (MANOVA) results (Since R2023b)