[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.

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

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

Significance 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

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.

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 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).

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