# Estimating HLM Models Using SPSS Menus: Part 4

Jeremy Albright

Posted on
ANOVA HLM

#### Intercepts- and Slopes-as-Outcomes Model

R&B present a final model that includes one further generalization of the random coefficients model. They begin again with the level-1 model:

$$$Y_{ij} = \beta_{0j} + \beta_{1j}(SES)+ e_{ij} \tag{6}$$$

The intercept $$\beta_{0j}$$ is now modeled as a function of the average SES level of the school and whether or not the school is public or private. The slope $$\beta_{1j}$$ is modeled in similar fashion.

$$$\beta_{0j} = \gamma_{00} + \gamma_{01}(MEAN\ SES)+ \gamma_{02}(SECTOR)+ u_{0j} \tag{10}$$$

$$$\beta_{1j} = \gamma_{10} + \gamma_{11}(MEAN\ SES)+ \gamma_{12}(SECTOR)+ u_{1j} \tag{11}$$$

Substituting (10) and (11) into (6) leads to the combined model:

$$$Y_{ij} = \gamma_{00} + \gamma_{01}(MEAN\ SES)+ \gamma_{02}(SECTOR) \\ + \gamma_{10}(SES) + \gamma_{11}(MEAN\ SES)(SES) \\ +\gamma_{12}(SECTOR)(SES) +u_{0j} + u_{1j}(SES)+ e_{ij} \tag{12}$$$

To estimate (12) in SPSS go to Analyze > Mixed Models > Linear. The Specify Subjects and Repeated menu appears again. As before, place schid in the Subjects box and leave Repeated blank.