Description of the dataset
We will be using a dataset on neighborhood effects for this assignment.These data are drawn from the Project on Human Development in Chicago Neighborhoods (PHDCN), a probability sample of individuals nested within 342 Chicago neighborhoods. The individual was interviewed with regard to conditions, events, and relationships within the local area defined as the neighborhood. The individual-level variables are derived from the interviews, and the neighborhood-level variables are derived from the 1990 census. Rob Sampson, a sociologist at Harvard, was interested in assessing whether informal social control mediates the relationship between neighborhood social composition and perceived violence.
1. Read the Sampson, Raudenbush, & Earls article in preparation for this assignment. It will provide the necessary background on the study and the variables of interest.
2. The data set you will use is in a folder called Sampson on the class website. In the folder, there is a data dictionary describing the variables and the level-1 (individuals) and level-2 (neighborhoods) files. Download the dictionary and the data.
3. Based on your reading of the article and the variable list, create one or two research questions that can be answered using an HLM model. The outcome variable is perceived violence, measured at the individual level. You need to consider what combination of individual and neighborhood characteristics best explains variation in perceived violence. 4. In SPSS, check for "missing" data in the level-1 file prior to reading the files into HLM. Review the distributions of each variable in both level-1 and level-2 files by creating plots in SPSS. Comment on the variable distributions - are any cause for concern due to unusual skewness?
5. Read in the two data files into HLM and create the mdm file.
6. In the basic specifications menu, check that you want a level-1 and level-2 residual file. Use full maximum likelihood for estimation.
7. Choose VIOLENCE as the outcome variable. Fit an unconditional (intercept-only) model to the Sampson data. Interpretin words the coefficient for the fixed effect and the variance components at both levels. Report the confidence interval and the plausible values interval for the fixed effect. What do these intervals tell you? How are they different?
8. Decompose the variance of perceived violence into the percent attributable to individuals and the percent attributable to neighborhoods. This is the intraclass correlation or ICC. Show your computation. How does this compare (in magnitude) to the ICC for the High School and Beyond data we used in class?
Fit2 conditional models to the Sampson data.
Model 1:For the first model, use an intercept-only model at level-1 but add one (or more predictors) at level-2. This is similar in form to the means-as-outcomes model on your scorecard that we discussed in class.
• How will you center each level-2 variable? Justify all decisions.
• Interpret both the fixed effects and the variance components.
• Using proportional reduction in variance calculations (comparing this model to the unconditional model), describe how much variation in the intercept is attributable to the predictor(s) you choose.
Model 2:For the second model, add a predictor or set of predictors at level-1 but keep the same predictors at level-2 that you chose for the first conditional model.
• How does this change the model from Model 1? What variables do you want to add to level-1? How will you center each variable? Justify all decisions.
• Do all level-1 coefficients vary across neighborhoods at level-2, or will some be fixed?
• Interpret all parameters in your second model, both the fixed effects and all the variance components, including the covariances. Describe the meaning of the gammas and the elements of TAUin words.
• For the second model, provide both a table of your estimates (both fixed effects, variance components, and deviance statistic) and a plot of your final model. You can consult papers on the class website or the HLM text for good examples of multilevel tables. The Garner paper on SPARK is a useful model, but you may find other examples in your own disciplines.
10. Output the level-1 and level-2 residual files from your final model.
• Examine the residual files and produce appropriate residual plots to examine the assumptions. Are the Level-1 residuals normally distributed? Are the level-2 residuals multivariate normal? How do you know?
• Sort in ascending order the level-2 empirical bayes coefficients that represent the mean violence for each neighborhood (ECINTRCPT1). Depending on how you centered the level-1 predictors in your model, these may be adjusted means (if you use grand-mean centering, you are adjusting for differences across people in that neighborhood on that predictor). Identify the 5 best and 5 worst neighborhoods. Then examine some descriptive information about these neighborhoods from the level-2 SPSS file. In terms of perceived violence, what characterizes neighborhoodsthat are doing the best? The worst?