Intermediate Econometrics - Coursework Example

Let and denote their unadjusted counterparts. Then; The answer is FALSE; in loglinear regression analysis is used to describe the pattern of data in a contingency table. A model is constructed to predict the natural log of the frequency of each cell in the contingency table. For a 2x2 table, that means the model is . So we can always say, as a simple function, that the coefficient represents an increase in the log of predicted counts. If , for instance, we could say that this model shows that factor increases the predicted log count by 2 (all other factors held constant).

The answer is TRUE; all the three tests (Wald test, Lagrange Multiplier, Likelihood ratio test) address the same basic question, which is, does constraining parameters to zero (i.e. leaving out the predictor variables) reduce the fit of the model? The null hypothesis for all three tests is that the smaller model is the "true" model, a large test statistics indicate that the null hypothesis is false. The only difference between the tests is how they go about answering that question. The graph below explains more on the relationship; The graph below illustrates what each of the three tests does.

Along the (labelled ) are possible values of the parameter . Along the are the values of the log likelihood corresponding to those values of a. The test compares the log likelihoods of a model with values of the parameter constrained to some value to a model where  is freely estimated. It does this by comparing the height of the likelihoods for the two models to see if the difference is statistically significant (having in mind, higher values of the likelihood indicate better fit). In the figure above, this corresponds to the vertical distance between the two dotted lines.

In contrast, the Wald test compares the parameter estimate  to ; where  is the value of  under the null hypothesis, which generally states that . If  is significantly different