Load the sample data.

load('weight.mat');

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.

tbl = table(InitialWeight,Program,Subject,Week,y);
tbl.Subject = nominal(tbl.Subject);
tbl.Program = nominal(tbl.Program);

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

lme = fitlme(tbl,'y ~ InitialWeight + Program*Week + (Week|Subject)');

Compute the fitted values and raw residuals.

F = fitted(lme);
R = residuals(lme);

Plot the residuals versus the fitted values.

plot(F,R,'bx')
xlabel('Fitted Values')
ylabel('Residuals')

Now, plot the residuals versus the fitted values, grouped by program.

figure();
gscatter(F,R,Program)

The residuals seem to behave similarly across levels of the program as expected.

Load the sample data.

load carbig

Store the variables for miles per gallon (MPG), acceleration, horsepower, cylinders, and model year in a table.

tbl = table(MPG,Acceleration,Horsepower,Cylinders,Model_Year);

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

lme = fitlme(tbl,'MPG ~ Acceleration + Horsepower + Cylinders + (Acceleration|Model_Year)');

Compute the conditional Pearson residuals and display the first five residuals.

PR = residuals(lme,'ResidualType','Pearson');
PR(1:5)

ans = 5×1

   -0.0533
    0.0652
    0.3655
   -0.0106
   -0.3340

Compute the marginal Pearson residuals and display the first five residuals.

PRM = residuals(lme,'ResidualType','Pearson','Conditional',false);
PRM(1:5)

ans = 5×1

   -0.1250
    0.0130
    0.3242
   -0.0861
   -0.3006

Load the sample data.

load carbig

Store the variables for miles per gallon (MPG), acceleration, horsepower, cylinders, and model year in a table.

tbl = table(MPG,Acceleration,Horsepower,Cylinders,Model_Year);

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

lme = fitlme(tbl,'MPG ~ Acceleration + Horsepower + Cylinders + (Acceleration|Model_Year)');

Draw a histogram of the raw residuals with a normal fit.

r = residuals(lme);
histfit(r)

Normal distribution seems to be a good fit for the residuals.

Compute the conditional Pearson and standardized residuals and create box plots of all three types of residuals.

pr = residuals(lme,'ResidualType','Pearson');
st = residuals(lme,'ResidualType','Standardized');
X = [r pr st];
boxplot(X)

Red plus signs show the observations with residuals above or below $$q3+1.5(q3-q1)$$ and $$q1-1.5(q3-q1)$$, where $$q1$$ and $$q3$$ are the 25th and 75th percentiles, respectively.

Find the observations with residuals that are 2.5 standard deviations above and below the mean.

find(r > mean(r,'omitnan') + 2.5*std(r,'omitnan'))

ans = 7×1

    62
   252
   255
   330
   337
   341
   396

find(r < mean(r,'omitnan') - 2.5*std(r,'omitnan'))

ans = 3×1

   119
   324
   375