# Two Ways of Specifying Random Intercepts in SPSS’s Mixed Model

To do: Screenshots of SPSS dialogues.

In SPSS’s Mixed Models dialogue, there are two ways to enter random intercepts, either by the Subjects and Repeated measures dialogue (the first window upon opening the dialogue) or the Random subdialogue. This document shows how to generate identical results using either option.

We’ll use R to get the data, demostrate the model we’re trying to fit, and export the data for SPSS. The data comes from Brady West.

library("tidyverse")
ratpup <- readr::read_delim("http://www-personal.umich.edu/~bwest/rat_pup.dat", "\t")

Make the treatment binary, and convert both it and sex to numeric.

ratpup <- ratpup %>%
mutate(treat = (treatment != "Control") + 0) %>%
mutate(female = (sex == "Female") + 0) %>%
select(-c(treatment, sex)) %>%
as.data.frame()

Write the data into SPSS

library("foreign")
write.foreign(ratpup, datafile = "ratpup.sav",
codefile = "ratpup.sps", package = "SPSS")

The mixed model we’ll be fitting has a random intercept per litter:

## SPSS

Open the file ratpup.sps and run the code to load the data.

We’ll run two variations using the dialogue Analyze -> Mixed Models -> Linear.

First, ignore the first screen. Place weight in Dependent variable; treat, female and litter into Factors, and litsize into Covariates. In the Fixed subdialogue, enter the main effect for litsize and the main and interaction of treat and female. In the Random subdialogue, place litter into the Model. Do not check the box “Include intercept”.

This dialogue should produce the following syntax:

MIXED weight BY female litter treat WITH litsize
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001)
HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=female treat female*treat litsize | SSTYPE(3)
/METHOD=REML
/PRINT=SOLUTION
/RANDOM=litter | COVTYPE(VC).

In this model, litter was chosen as “subject” in the first screen. Random Intercept was included but not litter, and litter was included in “Subject groupings”

Next, we’ll make use of the first screen. In the first screen, place little into Subjects. Enter the variables as described above. litter does not have to be placed in Factors anymore, but it will not affect anything if it is. In the Random subdialogue, check “Include intercept”. Do not enter litter into Model, but at the bottom under Subject Groups, enter it into Combinations.

The syntax is:

MIXED weight BY female treat WITH litsize
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001)
HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=female treat female*treat litsize | SSTYPE(3)
/METHOD=REML
/PRINT=SOLUTION
/RANDOM=INTERCEPT | SUBJECT(litter) COVTYPE(VC).

The difference is highlighted in red; specifically

/RANDOM=litter | COVTYPE(VC).

versus

/RANDOM=INTERCEPT | SUBJECT(litter) COVTYPE(VC).

but both models are identical.