# predict

Compute predicted values given predictor values

## Description

returns
the predicted values from the repeated measures model `ypred`

= predict(`rm`

,`tnew`

,`Name,Value`

)`rm`

with
additional options specified by one or more `Name,Value`

pair
arguments.

For example, you can specify the within-subjects design matrix.

## Examples

### Predict Response Values

Load the sample data.

`load fisheriris`

The column vector `species`

consists of iris flowers of three different species: setosa, versicolor, and virginica. The double matrix `meas`

consists of four types of measurements on the flowers: the length and width of sepals and petals in centimeters, respectively.

Store the data in a table array.

t = table(species,meas(:,1),meas(:,2),meas(:,3),meas(:,4), ... 'VariableNames',{'species','meas1','meas2','meas3','meas4'}); Meas = dataset([1 2 3 4]','VarNames',{'Measurements'});

Fit a repeated measures model, where the measurements are the responses and the species is the predictor variable.

rm = fitrm(t,'meas1-meas4~species','WithinDesign',Meas);

Predict responses for the three species.

Y = predict(rm,t([1 51 101],:))

`Y = `*3×4*
5.0060 3.4280 1.4620 0.2460
5.9360 2.7700 4.2600 1.3260
6.5880 2.9740 5.5520 2.0260

### Predict Response Values and Plot Predictions

Load the sample data.

`load longitudinalData`

The matrix `Y`

contains response data for 16 individuals. The response is the blood level of a drug measured at five time points (time = 0, 2, 4, 6, and 8). Each row of `Y`

corresponds to an individual, and each column corresponds to a time point. The first eight subjects are female, and the second eight subjects are male. This is simulated data.

Define a variable that stores gender information.

Gender = ['F' 'F' 'F' 'F' 'F' 'F' 'F' 'F' 'M' 'M' 'M' 'M' 'M' 'M' 'M' 'M']';

Store the data in a proper table array format to perform repeated measures analysis.

t = table(Gender,Y(:,1),Y(:,2),Y(:,3),Y(:,4),Y(:,5), ... 'VariableNames',{'Gender','t0','t2','t4','t6','t8'});

Define the within-subjects variable.

Time = [0 2 4 6 8]';

Fit a repeated measures model, where the blood levels are the responses and gender is the predictor variable.

rm = fitrm(t,'t0-t8 ~ Gender','WithinDesign',Time);

Predict the responses at intermediate times.

time = linspace(0,8)'; Y = predict(rm,t([1 5 8 12],:), ... 'WithinModel','orthogonalcontrasts','WithinDesign',time);

Plot the predictions along with the estimated marginal means.

plotprofile(rm,'Time','Group',{'Gender'}) hold on; plot(time,Y,'Color','k','LineStyle',':'); legend('Gender=F','Gender=M','Predictions') hold off

### Compute and Plot Confidence Intervals

Load the sample data.

`load longitudinalData`

The matrix `Y`

contains response data for 16 individuals. The response is the blood level of a drug measured at five time points (time = 0, 2, 4, 6, and 8). Each row of Y corresponds to an individual, and each column corresponds to a time point. The first eight subjects are female, and the second eight subjects are male. This is simulated data.

Define a variable that stores gender information.

Gender = ['F' 'F' 'F' 'F' 'F' 'F' 'F' 'F' 'M' 'M' 'M' 'M' 'M' 'M' 'M' 'M']';

Store the data in a proper table array format to perform repeated measures analysis.

t = table(Gender,Y(:,1),Y(:,2),Y(:,3),Y(:,4),Y(:,5), ... 'VariableNames',{'Gender','t0','t2','t4','t6','t8'});

Define the within-subjects variable.

Time = [0 2 4 6 8]';

Fit a repeated measures model, where the blood levels are the responses and gender is the predictor variable.

rm = fitrm(t,'t0-t8 ~ Gender','WithinDesign',Time);

Predict the responses at intermediate times.

time = linspace(0,8)'; [ypred,ypredci] = predict(rm,t([1 5 8 12],:), ... 'WithinModel','orthogonalcontrasts','WithinDesign',time);

Plot the predictions and the confidence intervals for predictions along with the estimated marginal means.

p1 = plotprofile(rm,'Time','Group',{'Gender'}); hold on; p2 = plot(time,ypred,'Color','k','LineStyle',':'); p3 = plot(time,ypredci(:,:,1),'k--'); p4 = plot(time,ypredci(:,:,2),'k--'); legend([p1;p2(1);p3(1)],'Gender=F','Gender=M','Predictions','Confidence Intervals') hold off

## 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`

.

`tnew`

— New data

table used to create `rm`

(default) | table

New data including the values of the response variables and
the between-subject factors used as predictors in the repeated measures
model, `rm`

, specified as a table. `tnew`

must
contain all of the between-subject factors used to create `rm`

.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`ypred = predict(rm,tnew,'alpha',0.01)`

`Alpha`

— Significance level

0.05 (default) | scalar value in the range of 0 through 1

Significance level of the confidence intervals for the predicted
values, specified as the comma-separated pair consisting of
`'alpha'`

and a scalar value in the range of 0 to
1. The confidence level is 100*(1–`alpha`

)%.

**Example: **`'alpha',0.01`

**Data Types: **`double`

| `single`

`WithinModel`

— Model for within-subject factors

`'separatemeans'`

| `'orthogonalcontrats'`

| character vector | string scalar

Model for the within-subject factors, specified as the comma-separated
pair consisting of `'WithinModel'`

and one of the
following:

`'separatemeans'`

— Compute a separate mean for each group.`'orthogonalcontrasts'`

— Valid when the within-subject design consists of a single numeric factor*T*. This specifies a model consisting of orthogonal polynomials up to order*T*^{(r-1)}, where*r*is the number of repeated measures.A character vector or string scalar that defines a model specification in the within-subject factors.

**Example: **`'WithinModel','orthogonalcontrasts'`

**Data Types: **`char`

| `string`

`WithinDesign`

— Design for within-subject factors

vector | matrix | table

Design for within-subject factors, specified as the comma-separated
pair consisting of `'WithinDesign'`

and a vector,
matrix, or a table. It provides the values of the within-subject factors
in the same form as the `RM.WithinDesign`

property.

**Example: **`'WithinDesign','Time'`

**Data Types: **`single`

| `double`

| `table`

## Output Arguments

`yci`

— Confidence intervals for predicted values

*n*-by-*r*-by-2 matrix

Confidence intervals for predicted values from the repeated
measures model `rm`

, returned as an *n*-by-*r*-by-2
matrix.

These are nonsimultaneous intervals for predicting the mean
response at the specified predictor values. For predicted value `ypred(i,j)`

,
the lower limit of the interval is `yci(i,j,1)`

and
the upper limit is `yci(i,j,2)`

.

## Version History

**Introduced in R2014a**

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