Example L5 Ordered response model

 

In this example we analyse ordinal data on changes in the severity of Schizophrenia in data from the National Institute of Mental Health (NIMH), see Rabe-Hesketh and Skrondal (2005, Ch 5). Patients were randomly allocated to 1 of 4 treatments (Placebo, Chlorpromazine, Fluphenazine, Thioridazine) and examined weekly for up to 6 weeks. The data have previously been analysed by Hedeker and Gibbons (1996a), Gibbons et al. (1998) and Gibbons and Hedeker (1994). In this example we follow Rabe-Hesketh and Skrondal (2005, Ch 5) and combine the treatments Chlorpromazine, Fluphenazine and Thioridazine.

 

 

Data description

 

Number of observations (rows): 1603

Number of variables (columns): 8

 

Variables:

 

id=subject identifier

week=week (0,1,2,,6) of assessment since randomisation to treatment;

imps=score on item 79 of the Inpatient Multidimensional Psychiatric Scale (IMPS) of Lorr and Klextt (1966).

treatment=1 if subject was in the treatment group (drug), 0 otherwise;

 

Following Rabe-Hesketh and Skrondal (2005, Ch 5) and Hedeker and Gibbons (1996a) we recode the imps variable into impso, an ordinal variable with 4 categories, i.e.

 

impso=1 if 1<=imps<=2.4;

impso=2 if 2.5<=imps<4.4

impso=3 if 4.5<=imps<=5.4

impso=4 if 5.5<=imps<=7

 

Following Rabe-Hesketh and Skrondal (2005, Ch 5) we also use the square root of week (weeksqrt) instead of week in its raw form as an explanatory variable. Similarly we also produce a new variable from the interaction (interact) of weeksqrt and treatment.

 

 

References

 

Gibbons, R. D., Hedeker, C., Waterneaux, C., & Davis, J.M., (1988), Random regression models: A comprehensive approach to the analysis of longitudinal psychiatric data, Psychopharmacology Bulletin, 24, 438-443

Gibbons, R. D., & Hedeker, C., (1994), Application of random effects probit regression models, Journal of Consulting and Clinical Psyschology.

Hedeker, D., & Gibbons, R.D., (1996), Applied longitudinal data anlaysis, Chichester, UK, Wiley

Rabe-Hesketh, S., and Skrondal, A., (2005), Multilevel and Longitudinal Modelling using Stata, Stata Press, Stata Corp, College Station, Texas.

 

 

 

 

The first few lines of schiz.dat look like

 

 

 

Sabre commands

 

out schiz.log

trace schiz.trace

data id imps week treatment sex weeksqrt interact impso

read schiz.dat

case id

yvar impso

ordered y

lfit weeksqrt treatment interact

dis m

dis e

fit weeksqrt treatment interact

dis m

dis e

stop

 

 

 

Sabre log file

 

<S> trace schiz.trace

<S> data id imps week treatment sex weeksqrt interact impso

<S> read schiz.dat

 

1603 observations in dataset

 

<S> case id

<S> yvar impso

<S> ordered y

<S> lfit weeksqrt treatment interact

 

Iteration Log. lik. Step End-points Orthogonality

length 0 1 criterion

________________________________________________________________________

1 -2239.6731 1.0000 fixed fixed 18.971

2 -1947.5622 0.5000 fixed fixed 46.248

3 -1885.7509 1.0000 fixed fixed 131.39

4 -1879.9699 1.0000 fixed fixed 248.84

5 -1878.6522 1.0000 fixed fixed 1158.2

6 -1878.2740 1.0000 fixed fixed 253.33

7 -1878.0969 1.0000 fixed fixed 54.836

8 -1878.0969 1.0000 fixed fixed

 

<S> dis m

 

X-vars Y-var

______________________________

weeksqrt impso

treatment

interact

 

Univariate model

Standard ordered logit

 

Number of observations = 1603

 

X-var df = 3

 

Log likelihood = -1878.0969 on 1600 residual degrees of freedom

 

<S> dis e

 

Parameter Estimate Std. Err.

___________________________________________________

weeksqrt -0.53665 0.11081

treatment -0.60428E-03 0.18833

interact -0.75097 0.12768

cut1 -3.8073 0.18986

cut2 -1.7602 0.17027

cut3 -0.42211 0.16363

 

<S> fit weeksqrt treatment interact

 

Initial Homogeneous Fit:

 

Iteration Log. lik. Step End-points Orthogonality

length 0 1 criterion

________________________________________________________________________

1 -2239.6731 1.0000 fixed fixed 18.971

2 -1947.5622 0.5000 fixed fixed 46.248

3 -1885.7509 1.0000 fixed fixed 131.39

4 -1879.9699 1.0000 fixed fixed 248.84

5 -1878.6522 1.0000 fixed fixed 1158.2

6 -1878.2740 1.0000 fixed fixed 253.33

7 -1878.0969 1.0000 fixed fixed 54.836

8 -1878.0969 1.0000 fixed fixed

 

 

Iteration Log. lik. Step End-points Orthogonality

length 0 1 criterion

________________________________________________________________________

1 -1775.2726 1.0000 fixed fixed 14.707

2 -1717.2806 1.0000 fixed fixed 12.350

3 -1703.2212 1.0000 fixed fixed 119.24

4 -1701.5195 1.0000 fixed fixed 340.03

5 -1701.2283 1.0000 fixed fixed 337.78

6 -1701.1745 1.0000 fixed fixed 211.94

7 -1701.1622 1.0000 fixed fixed 18.610

8 -1701.1622 1.0000 fixed fixed

 

<S> dis m

 

X-vars Y-var Case-var

________________________________________________

weeksqrt impso id

treatment

interact

 

Univariate model

Standard ordered logit

Gaussian random effects

 

Number of observations = 1603

Number of cases = 437

 

X-var df = 3

Scale df = 1

 

Log likelihood = -1701.1622 on 1599 residual degrees of freedom

 

<S> dis e

 

Parameter Estimate Std. Err.

___________________________________________________

weeksqrt -0.76775 0.13107

treatment -0.81896E-01 0.31086

interact -1.2069 0.15280

cut1 -5.8917 0.33345

cut2 -2.8572 0.28969

cut3 -0.73532 0.27343

scale 1.9520 0.12113

 

<S> stop