**Exercise C2, linear
model**

Garner and Raudenbush (1991) and Raudenbush and Bryk (2002) studied the role of school and neighbourhood effects on educational attainment. The data set they used (neighbourhood.dat) was for young people who left school between 1984 and 1986 from one Scottish Educational uthority. The same data were used by Rabe-Hesketh and Skrondal (2005, exercise 2.2).

**Data description**

Number of observations (rows): 2310

Number of variables (columns): 12

Variables:

neighid=respondent’s neighbourhood identifier

schid= respondent’s schools identifier

attain=respondent’s combined end of school educational attainment as measured by grades from various exams

p7vrq=respondent’s verbal reasoning quotient as measured by a test at age 11-12 in primary school

p7read=respondent’s reading test score as measured by a test at age 11-12 in primary school

dadocc=respondent’s father’s occupation

dadunemp= 1 if respondent’s father unemployed, 0 otherwise

daded=1 if respondent’s father was in full time education after age 15, 0 otherwise

momed=1 if respondent’s mother was in full time education after age 15, 0 otherwise

male=1 if respondent is male, 0 otherwise

deprive= index of social deprivation for the local community in which the respondent lived

dummy=1 to 4; representing
collections of the schools or neighbourhoods

The first few lines of the data look like:

We can use both the school identifier (schid=0,1,2,…,20) and the neighbourhood identifier (neighid) as alternative random effects in this data set.

Start **Sabre** and
specify transcript file:

out neighborhood.log

data neighid
schid attain p7vrq p7read dadocc
dadunemp daded momed male &

deprive dummy

read neighborhood.dat

**Suggested exercise:**

(1) Estimate a linear model on attainment (attain) without covariates

(2) Allow for the school random effect (schid), use mass 64. Is this random effect significant?

(3) Add the observed student specific effects, with the starting values sigma 0.7, scale 0.1. How does the magnitude of the school random effect change?

(4) Add the neigbhourhood effect (deprive), with the starting values, sigma 0.7, scale 0.1 How does the magnitude of the school random effect change?

A data set sorted by the neighbourhood identifier (neighid); has been made available for you, this data set is called neighbourhood2.dat. To analyse this new data set type:

data neighid
schid attain p7vrq p7read dadocc
dadunemp daded momed male &

deprive dummy

read neighborhood2.dat

(6) Re-estimate the constant only model allowing for neighbourhood random effect (neighid), use mass 64. Is there a significant neighd random effect?

(7) Add the student specific effects, how does the magnitude of the neighid random effect change?

(8) Add observed neighbourhood effect deprive to the model, how does the magnitude of the neighid random effect change?

(9) What do the results of using either the schid or the neighid random effects tell you about what effects are needed in the modelling of attainment with this data set?

(10) What do the two sets of results show/suggest?

**References**

Garner, C. L., and Raudenbush, S. W., (1991), Neighbourhood effects on educational attainment: A multilevel analysis of the influence of pupil ability, family, school and neighbourhood, Sociology of education, 64, 252-262

Raudenbush, S. W., and Bryk, A. S., (2002), Hierarchical
Linear Models, Sage,

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