Concept Comprehension: Maximum Likelihood

Various items missing from earlier version of this given material that was skipped. These can be found in the original md-pset file for this problem set.

1. Your instructor noted that maximum likelihood models typically use an iterative process to compute estimates, rather than being able to compute estimates directly (aka analytically). What does iterative mean in this context? [1]

2. Consider a model in which the outcome is \(\texttt{eviction}\). For a person in the sample who was not evicted, their \(\mathbf{x}\mathbf{\beta}\) from a logit model was -2.90. What is the log-likelihood for this person (i.e., for this observation)? Explain/show the calculations by which you arrived at this number. [2]

3. Say you conduct a program evaluation of 1000 people and the standard error for one of your key estimates of the effect of the social program is 1. Your sponsor says this is much too imprecise and asks you how big the study would have to be to reduce the standard error to .25. If N = 1000 yielded an standard error of 1, approximately how large would the program evaluation study have to produce a standard error of .25? How do you know? [1]

4. In R, I fit a maximum likelihood model and R reports a deviance of 10089.6. What was the log-likelihood for this model? [1]

5. In R, I fit a model that has 10 parameters with a sample size of 5,620. The deviance is 10089.6. What will the AIC be for this model? What will the BIC be? [2]

6. I fit an alternative version of the previous model that adds 2 parameters, so 12 in all. The AIC for the new model is 10056.4, and the BIC by 10136.0. By each of these criteria, which model is preferred: Model #1 or Model #2? How do you know? [1]