coeftest

Linear hypothesis test on coefficients of repeated measures model

Syntax

tbl = coeftest(rm,A,C,D)

Description

tbl = coeftest(rm,A,C,D) returns a table tbl containing the multivariate analysis of variance (manova) for the repeated measures model rm.

Examples

Test Coefficients for First and Last Repeated Measures

Load the sample data.

load repeatedmeas

The table between includes the between-subject variables age, IQ, group, gender, and eight repeated measures y1 through y8 as responses. The table within includes the within-subject variables w1 and w2. This is simulated data.

Fit a repeated measures model, where the repeated measures y1 through y8 are the responses, and age, IQ, group, gender, and the group-gender interaction are the predictor variables. Also specify the within-subject design matrix.

rm = fitrm(between,'y1-y8 ~ Group*Gender + Age + IQ','WithinDesign',within);

Test that the coefficients of all terms in the between-subjects model are the same for the first and last repeated measurement variable.

coeftest(rm,eye(8),[1 0 0 0 0 0 0 -1]')

ans=4×7 table
    Statistic     Value       F       RSquare    df1    df2    pValue 
    _________    _______    ______    _______    ___    ___    _______

    Pillai        0.3355    1.3884    0.3355      8     22     0.25567
    Wilks         0.6645    1.3884    0.3355      8     22     0.25567
    Hotelling    0.50488    1.3884    0.3355      8     22     0.25567
    Roy          0.50488    1.3884    0.3355      8     22     0.25567

The $$p$$-value of 0.25567 indicates that there is not enough statistical evidence to conclude that the coefficients of all terms in the between-subjects model for the first and last repeated measures variable are different.

Input Arguments

rm — Repeated measures model

RepeatedMeasuresModel object

Repeated measures model, returned as a RepeatedMeasuresModel object.

For properties and methods of this object, see RepeatedMeasuresModel.

A — Specification representing between-subjects model

a-by-p matrix

Specification representing the between-subjects model, specified as an a-by-p numeric matrix, with rank a ≤ p.

Data Types: single | double

C — Specification representing within-subjects hypothesis

r-by-c matrix

Specification representing the within-subjects (within time) hypotheses, specified as an r-by-c numeric matrix, with rank c ≤ r ≤ n – p.

Data Types: single | double

D — Hypothesized value

0 (default) | scalar value | a-by-c matrix

Hypothesized value, specified as a scalar value or an a-by-c matrix.

Data Types: single | double

Output Arguments

tbl — Results of multivariate analysis of variance

table

Results of multivariate analysis of variance for the repeated measures model rm, returned as a table containing the following columns.

Statistic	Type of test statistic used
Value	Value of the corresponding test statistic
F	F-statistic value
RSquare	Measure of variance explained
df1	Numerator degrees of freedom for the F-statistic
df2	Denominator degrees of freedom for the F-statistic
pValue	p-value associated with the test statistic value

Tips

• This test is defined as A*B*C = D, where B is the matrix of coefficients in the repeated measures model. A and C are numeric matrices of the proper size for this multiplication. D is a scalar or numeric matrix of the proper size. The default is D = 0.

Version History

Introduced in R2014a