5 Random Coefficients Model 1

5.1 MODEL 1

• SPSS implementation is very similar to those presented earlier ( Analysis of Paired Data: LMM ).

• Note the difference in the Factor and Covariates and how we can include the Main Effects in the Fixed Effects dialog box.

• The LMM considers the random intercept and slope with time

• The main difference in the model implementation will be defining the random effect term.

• The Model 1 considers the correlation between the intercept and slope, i.e. the correlation between the random intercept and slope is zero.

• We will fit a model without interaction term for Group and Time, i.e. only including the main effects and without any interaction terms

The $G$ matrix for Model 1 is given by:

$$\begin{bmatrix} \sigma_{intP}^2 & \sigma_{intP, slopeP} \\ \sigma_{intP, slopeP} & \sigma_{slopeP}^2 \\ \end{bmatrix}$$

5.1.1 SPSS: Menu

5.1.2 SPSS: Script

# Unstructured    

MIXED SBP BY Sex Group WITH SBP0 Age BMI Time 
  /CRITERIA = DFMETHOD(SATTERTHWAITE) CIN(95) MXITER(100) MXSTEP(10) 
    SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) 
    LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE) 
  /FIXED = Sex Group SBP0 Age BMI Time | SSTYPE(3) 
  /METHOD = REML 
  /PRINT = G R SOLUTION 
  /RANDOM = INTERCEPT Time | SUBJECT(ID) COVTYPE(UN)