# margmean

Class: RepeatedMeasuresModel

Estimate marginal means

## Syntax

• `tbl = margmean(rm,vars)` example
• `tbl = margmean(rm,vars,'alpha',alpha)` example

## Description

example

````tbl = margmean(rm,vars)` returns the estimated marginal means for the variables `vars`, in the table `tbl`.```

example

````tbl = margmean(rm,vars,'alpha',alpha)` returns the 100*(1–`alpha`)% confidence intervals for the marginal means.```

## Input Arguments

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### `rm` — Repeated measures model`RepeatedMeasuresModel` object

Repeated measures model, returned as a `RepeatedMeasuresModel` object.

For properties and methods of this object, see `RepeatedMeasuresModel`.

### `vars` — Variables for which to compute the marginal meansstring | cell array of strings

Variables for which to compute the marginal means, specified as a string representing the name of a between or within-subjects factor in `rm`, or a cell array of strings representing the names of multiple variables. Each between-subjects factor must be categorical.

For example, if you want to compute the marginal means for the variables Drug and Gender, then you can specify as follows.

Example: `{'Drug','Gender'}`

Data Types: `char` | `cell`

### `alpha` — Confidence level0.05 (default) | scalar value in the range of 0 to 1

Confidence level of the confidence intervals for population marginal means, specified as a scalar value in the range of 0 to 1. The confidence level is 100*(1–`alpha`)%.

For example, you can specify a 99% confidence level as follows.

Example: `'alpha',0.01`

Data Types: `double` | `single`

## Output Arguments

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### `tbl` — Estimated marginal meanstable

Estimated marginal means, returned as a table. `tbl` contains one row for each combination of the groups of the variables you specify in `vars`, one column for each variable, and the following columns.

Column nameDescription
`Mean`Estimated marginal means
`StdErr`Standard errors of the estimates
`Lower`Lower limit of a 95% confidence interval for the true population mean
`Upper`Upper limit of a 95% confidence interval for the true population mean

## Examples

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### Compute Marginal Means Grouped by Two Factors

`load repeatedmeas`

The table `between` includes the between-subject variables age, IQ, group, gender, and eight repeated measures y1 to 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 to 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); ```

Compute the marginal means grouped by the between-subjects factor `Group` and the within-subject factor `Time`.

`M = margmean(rm,{'Group' 'Time'})`
```M = Group Time Mean StdErr Lower Upper _____ ____ _______ ______ ________ _______ A 1 20.03 11.966 -4.7859 44.846 A 2 5.8101 8.0942 -10.976 22.597 A 3 20.694 5.1928 9.9247 31.463 A 4 16.802 5.1693 6.0813 27.522 A 5 13.157 6.2678 0.15862 26.156 A 6 0.38527 5.8028 -11.649 12.42 A 7 8.1398 6.4472 -5.2309 21.51 A 8 11.057 7.6083 -4.7213 26.836 B 1 23.768 11.816 -0.73653 48.273 B 2 16.846 7.9927 0.26973 33.422 B 3 -4.0888 5.1276 -14.723 6.5453 B 4 2.0001 5.1045 -8.5858 12.586 B 5 8.6458 6.1892 -4.1898 21.481 B 6 -9.3054 5.73 -21.189 2.578 B 7 8.8204 6.3663 -4.3825 22.023 B 8 9.4889 7.5129 -6.0918 25.07 C 1 19.951 12.236 -5.4261 45.327 C 2 23.63 8.2771 6.4646 40.796 C 3 -22.121 5.3101 -33.133 -11.109 C 4 -14.307 5.2861 -25.27 -3.3443 C 5 -20.138 6.4094 -33.43 -6.8456 C 6 -28.583 5.9339 -40.889 -16.277 C 7 -25.273 6.5928 -38.946 -11.6 C 8 -21.836 7.7801 -37.971 -5.7009```

Display the description for table M.

`M.Properties.Description`
```ans = Estimated marginal means Means computed with Age=13.7, IQ=98.2667```

### Compute Estimated Marginal Means and Confidence Intervals

`load fisheriris`

The column vector, `species`, consists of iris flowers of three different species, setosa, versicolor, 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);`

Compute the marginal means grouped by the factor species.

`margmean(rm,'species')`
```ans = species Mean StdErr Lower Upper ____________ ______ ________ ______ ______ 'setosa' 2.5355 0.042807 2.4509 2.6201 'versicolor' 3.573 0.042807 3.4884 3.6576 'virginica' 4.285 0.042807 4.2004 4.3696```

`StdError` field shows the standard errors of the estimated marginal means. The `Lower` and `Upper` fields show the lower and upper bounds for the 95% confidence intervals of the group marginal means, respectively. None of the confidence intervals overlap, which indicates that marginal means differ with species. You can also plot the estimated marginal means using the `plotprofile` method.

Compute the 99% confidence intervals for the marginal means.

`margmean(rm,'species','alpha',0.01)`
```ans = species Mean StdErr Lower Upper ____________ ______ ________ ______ ______ 'setosa' 2.5355 0.042807 2.4238 2.6472 'versicolor' 3.573 0.042807 3.4613 3.6847 'virginica' 4.285 0.042807 4.1733 4.3967```