[beta,betanames]
= fixedEffects(lme) also returns the
names of estimated fixed-effects coefficients in betanames.
Each name corresponds to a fixed-effects coefficient in beta.

[beta,betanames,stats]
= fixedEffects(lme) also returns the
estimated fixed-effects coefficients of the linear mixed-effects model lme and
related statistics in stats.

[beta,betanames,stats]
= fixedEffects(lme,Name,Value) also
returns the estimated fixed-effects coefficients of the linear mixed-effects
model lme and related statistics with additional
options specified by one or more Name,Value pair
arguments.

lme — Linear mixed-effects model LinearMixedModel object

Linear mixed-effects model, returned as a LinearMixedModel object.

For properties and methods of this object, see LinearMixedModel.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments.
Name is the argument
name and Value is the corresponding
value. Name must appear
inside single quotes (' ').
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN.

'Alpha' — Confidence level 0.05 (default) | scalar value in the range 0 to 1

Confidence level, specified as the comma-separated pair consisting
of 'Alpha' and a scalar value in the range 0 to
1. For a value α, the confidence level is 100*(1–α)%.

For example, for 99% confidence intervals, you can specify the
confidence level as follows.

Example: 'Alpha',0.01

Data Types: single | double

'DFMethod' — Method for computing approximate degrees of freedom 'residual' (default) | 'satterthwaite' | 'none'

Method for computing approximate degrees of freedom for the t-statistic
that tests the fixed-effects coefficients against 0, specified as
the comma-separated pair consisting of 'DFMethod' and
one of the following.

'residual'

Default. The degrees of freedom are assumed to be constant
and equal to n – p, where n is
the number of observations and p is the number
of fixed effects.

'satterthwaite'

Satterthwaite approximation.

'none'

All degrees of freedom are set to infinity.

For example, you can specify the Satterthwaite approximation
as follows.

Fixed-effects coefficients estimates of the fitted linear mixed-effects
model lme, returned as a vector.

betanames — Names of fixed-effects coefficients table

Names of fixed-effects coefficients in beta,
returned as a table.

stats — Fixed-effects estimates and related statistics dataset array

Fixed-effects estimates and related statistics, returned as
a dataset array that has one row for each of the fixed effects and
one column for each of the following statistics.

Name

Name of the fixed effect coefficient

Estimate

Estimated coefficient value

SE

Standard error of the estimate

tStat

t-statistic for a test that the coefficient
is zero

DF

Estimated degrees of freedom for the t-statistic

pValue

p-value for the t-statistic

Lower

Lower limit of a 95% confidence interval for the fixed-effect
coefficient

Upper

Upper limit of a 95% confidence interval for the fixed-effect
coefficient

Display Fixed-Effects Coefficient Estimates and Names

Navigate to a folder containing sample data.

cd(matlabroot)
cd('help/toolbox/stats/examples')

Load the sample data.

load weight

The data set weight contains data from a
longitudinal study, where 20 subjects are randomly assigned to 4 exercise
programs, and their weight loss is recorded over six 2-week time periods.
This is simulated data.

Store the data in a table. Define Subject and Program as
categorical variables.

Fit a linear mixed-effects model where the initial weight,
type of program, week, and the interaction between week and program
are the fixed effects. The intercept and week vary by subject.

Compute Coefficient Estimates and Related Statistics

Load the sample data.

load carbig

Fit a linear mixed-effects model for miles per gallon
(MPG), with fixed effects for acceleration and horsepower, and potentially
correlated random effects for intercept and acceleration grouped by
model year. First, store the data in a table.

The small p-values (under pValue)
indicate that all fixed-effects coefficients are significant.

Compute Confidence Intervals with Specified Options

Navigate to a folder containing sample data.

cd(matlabroot)
cd('help/toolbox/stats/examples')

Load the sample data.

load shift

The data shows the deviations from the target quality characteristic
measured from the products that five operators manufacture during
three shifts: morning, evening, and night. This is a randomized block
design, where the operators are the blocks. The experiment is designed
to study the impact of the time of shift on the performance. The performance
measure is the deviation of the quality characteristics from the target
value. This is simulated data.

Fit a linear mixed-effects model with a random intercept
grouped by operator to assess if performance significantly differs
according to the time of the shift.

Compute the 99% confidence intervals for fixed-effects
coefficients, using the residual method to compute the degrees of
freedom. This is the default method.

The Satterthwaite approximation usually produces smaller DF values
than the residual method. That is why it produces larger p-values
(pValue) and larger confidence intervals (see Lower and Upper).