## Stata 15 help for manova

```
[MV] manova -- Multivariate analysis of variance and covariance

Syntax

manova depvarlist = termlist [if] [in] [weight] [, options]

where termlist is a factor-variable list with the following additional
features:

o Variables are assumed to be categorical; use the c. factor-variable
operator to override this.
o The | symbol (indicating nesting) may be used in place of the #
symbol (indicating interaction).
o The / symbol is allowed after a term and indicates that the
following term is the error term for the preceding terms.

options                  Description
-------------------------------------------------------------------------
Model
noconstant             suppress constant term
dropemptycells         drop empty cells from the design matrix
-------------------------------------------------------------------------
bootstrap, by, jackknife, and statsby are allowed; see prefix.
Weights are not allowed with the bootstrap prefix.
aweights are not allowed with the jackknife prefix.
aweights and fweights are allowed; see weight.
See [MV] manova postestimation for features available after estimation.

Statistics > Multivariate analysis > MANOVA, multivariate regression, and
related > MANOVA

Description

The manova command fits multivariate analysis-of-variance (MANOVA) and
multivariate analysis-of-covariance (MANCOVA) models for balanced and
unbalanced designs, including designs with missing cells, and for
factorial, nested, or mixed designs, or designs involving repeated
measures.

The mvreg command will display the coefficients, standard errors, etc.,
of the multivariate regression model underlying the last run of manova.

See [R] anova for univariate ANOVA and ANCOVA models.  See [MV] mvtest
covariances for Box's test of MANOVA's assumption that the covariance
matrices of the groups are the same, and see [MV] mvtest means for
multivariate tests of means that do not make this assumption.

Options

+-------+
----+ Model +------------------------------------------------------------

noconstant suppresses the constant term (intercept) from the model.

dropemptycells drops empty cells from the design matrix.  If
c(emptycells) is set to keep (see set emptycells), this option
temporarily resets it to drop before running the MANOVA model.  If
c(emptycells) is already set to drop, this option does nothing.

Remarks

The # symbol indicates interaction.  The | symbol indicates nesting (a|b
is read "a is nested within b").  A / between terms indicates that the
term to the right of the slash is the error term for the terms to the
left of the slash.

Examples

---------------------------------------------------------------------------
Setup
. webuse metabolic

One-way MANOVA
. manova y1 y2 = group

View the underlying multivariate regression model
. mvreg

View the underlying multivariate regression model with 90% confidence
intervals and displaying the base categories
. mvreg, level(90) base

---------------------------------------------------------------------------
Setup
. webuse jaw

Two-way MANOVA
. manova y1 y2 y3 = gender fracture gender#fracture

The same model, but less typing
. manova y* = gender##fracture

---------------------------------------------------------------------------
Setup
. webuse videotrainer

Manova with nested data
. manova primary extra = video / store|video / associate|store|video
/, dropemptycells

---------------------------------------------------------------------------
Setup

Split-plot MANOVA
. manova score comp = pr / cl|pr sk pr#sk / cl#sk|pr / gr|cl#sk|pr /,
dropemptycells

---------------------------------------------------------------------------
Setup
. webuse biochemical

MANCOVA
. manova y1 y2 y3 = group c.x1 c.x2

---------------------------------------------------------------------------
Setup
. webuse nobetween
. gen mycons = 1

MANOVA with repeated measures data
. manova test1 test2 test3 = mycons, noconstant
. mat c = (1,0,-1 \ 0,1,-1)
. manovatest mycons, ytransform(c)
---------------------------------------------------------------------------

Stored results

manova stores the following in e():

Scalars
e(N)                number of observations
e(k)                number of parameters
e(k_eq)             number of equations in e(b)
e(df_m)             model degrees of freedom
e(df_r)             residual degrees of freedom
e(df_#)             degrees of freedom for term #
e(rank)             rank of e(V)

Macros
e(cmd)              manova
e(cmdline)          command as typed
e(depvar)           names of dependent variables
e(indepvars)        names of the right-hand-side variables
e(term_#)           term #
e(errorterm_#)      error term for term # (defined for terms using
nonresidual error)
e(wtype)            weight type
e(wexp)             weight expression
e(r2)               R-squared for each equation
e(rmse)             RMSE for each equation
e(F)                F statistic for each equation
e(p_F)              p-value for F test for each equation
e(properties)       b V
e(estat_cmd)        program used to implement estat
e(predict)          program used to implement predict
e(marginsnotok)     predictions disallowed by margins
e(marginsdefault)   default predict() specification for margins
e(asbalanced)       factor variables fvset as asbalanced
e(asobserved)       factor variables fvset as asobserved

Matrices
e(b)                coefficient vector (a stacked version of e(B))
e(B)                coefficient matrix
e(E)                residual-error SSCP matrix
e(xpxinv)           generalized inverse of X'X
e(H_m)              hypothesis SSCP matrix for the overall model
e(stat_m)           multivariate statistics for the overall model
e(eigvals_m)        eigenvalues of E^-1H for the overall model
e(aux_m)            s, m, and n values for the overall model
e(H_#)              hypothesis SSCP matrix for term #
e(stat_#)           multivariate statistics for term # (if computed)
e(eigvals_#)        eigenvalues of E^-1H for term # (if computed)
e(aux_#)            s, m, and n values for term # (if computed)
e(V)                variance-covariance matrix of the estimators

Functions
e(sample)           marks estimation sample

```