Consider the best fitting OLRM returned by the backward procedure Test its goodness of fit using an adequate test

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For all the variables, the value 0 represents a missing value. We want to test if there is an association between Q2 and the other variables in the data set using the ordered logistic regression model.

(1) Import the data. Recode the variable race so that all the categories having a frequency lower than 100 are combined into the category “other”. Replace the missing values in the data set with NA.

(2) Consider the OLRM intercept model having Q2 as the dependent variable (i.e., the OLRM without explanatory variables). Write down the model formula and compute the estimate of the intercept parameters without estimating the model.

(3) Use the backward selection procedure to select the best-fitting OLRM. The code we used in the practical session on OLRM returns an error. Explain why the error occurs and correct the code so that you can select the best-fitting model.

(4) Consider the best-fitting OLRM returned by the backward procedure. Test its goodness of fit using an adequate test.

(5) Interpret the model coefficients.

The assumption of parallel slopes (or proportional odds) underlying the OLRM implies that the coefficients describing the relationship between the ordinal dependent variable and the explanatory variables are the same between any pair of adjacent categories.

Develop a procedure to informal assess the assumption of parallel slopes.

(1) Describe the method and its logic.

(2) Consider the model estimated in Task 1, point 3. Apply the developed method to check if the parallel slopes assumption is tenable.

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