Example C2 Continuous response model

The data we use in this example are a sub-sample from the 1982 High School and Beyond Survey (Raudenbush, Bryk, 2002), and include information on 7,185 students nested within 160 schools: 90 public and 70 Catholic.  Sample sizes vary from 14 to 67 students per school.

Reference

Raudenbush, S.W., Bryk, A.S., 2002, Heirarchical Linear Models, Thousand Oaks, CA. Sage

Data description

Number of observations (rows): 7185

Number of variables (columns): 15

The variables include the following:

school=school identifier

student=student identifier

minority =1 if student is from an ethnic minority, 0 = other)

gender = 1 if student is female, 0 otherwise

ses = a standardized scale constructed from variables measuring parental education, occupation, and income, socio economic status

meanses = mean of the SES values for the students in this school

mathach= a measure of the students mathematics achievement

size = school enrolment

sector =1 if  school is from the Catholic sector, 0 = public

disclim = a scale measuring disciplinary climate

himnty =1 if more than 40% minority enrolment, 0 if less than 40%)

The first few lines of hsb.dat look like

Sabre commands

out hsb2.log

trace hsb2.trace

data school student minority gender ses meanses cses mathach size sector &

case school

yvar mathach

family g

constant cons

lfit minority gender ses meanses cons

dis m

dis e

mass 64

fit minority gender ses meanses cons

dis m

dis e

stop

Sabre log file

<S> trace hsb2.trace

<S> data school student minority gender ses meanses cses mathach size sector &

<S>      pracad desclim himinty meansesbycses sectorbycses

7185 observations in dataset

<S> case school

<S> yvar mathach

<S> family g

<S> constant cons

<S> lfit minority gender ses meanses cons

Iteration       Log. lik.       Difference

__________________________________________

1          -23285.328

<S> dis m

X-vars            Y-var

______________________________

cons              mathach

minority

gender

ses

meanses

Univariate model

Standard linear

Number of observations             =    7185

X-var df           =     5

Log likelihood =     -23285.328     on    7180 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

cons                    14.070          0.11710

minority               -2.3410          0.17381

gender                 -1.3200          0.14658

ses                     1.9551          0.11151

meanses                 2.8675          0.21311

sigma                   6.1857

<S> mass 64

<S> fit minority gender ses meanses cons

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -23285.328

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -23188.269        1.0000    fixed  fixed       99.892

2          -23173.011        1.0000    fixed  fixed       47.620

3          -23168.722        1.0000    fixed  fixed       106.51

4          -23167.251        1.0000    fixed  fixed       26.804

5          -23166.850        1.0000    fixed  fixed       30.410

6          -23166.721        1.0000    fixed  fixed       23.731

7          -23166.634        1.0000    fixed  fixed       42.577

8          -23166.634        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

cons              mathach           school

minority

gender

ses

meanses

Univariate model

Standard linear

Gaussian random effects

Number of observations             =    7185

Number of cases                    =     160

X-var df           =     5

Sigma df           =     1

Scale df           =     1

Log likelihood =     -23166.634     on    7178 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

cons                    14.048          0.17491

minority               -2.7282          0.20412

gender                 -1.2185          0.16082

ses                     1.9265          0.10844

meanses                 2.8820          0.36521

sigma                   5.9905          0.50554E-01

scale                   1.5480          0.11885

<S> stop