Reference no: EM132495799
Question 1. For this question, let's revisit the job satisfaction example that is shown below.
|
Income
|
|
Job Satisfaction
|
|
Total
|
|
Dissat
|
Little
|
Moderate
|
Very
|
|
< 5k
|
2
|
4
|
13
|
3
|
22
|
|
5k - 15k
|
2
|
6
|
22
|
4
|
34
|
|
15k - 25k
|
0
|
1
|
15
|
8
|
24
|
|
> 25k
|
0
|
3
|
13
|
8
|
24
|
|
Total
|
4
|
14
|
63
|
23
|
104
|
(a) Fit the hamar model that treats income and job satisfaction as nominal variables and alunmes independence, between the two of them. In other words, fit the following model
log (μij) = λ + λiI + λjS i = 1,2,3,4 j = 1,2,3,4
Using just the output from this model, can you perform a test of whether income and job satisfaction are independent? If so, perform the test. If not, explain what other information you would need to such a test.
(b) Both income and job satisfaction are ordinal variables, but the model in (a) ignores this information.
(i) Is the model from (a) a valid model for this data even though it ignore; the ordinality of the data?
(ii) Why could it be a good thing to incorporate the ordinality of these variables?
(c) Fit a model that incorporates the fact that both variables are ordinal.
(i) Write down your model and present the estimated coefficients from your model.
(ii) Use a likelihood ratio test to compare your model with the independence model in (a)
(iii) Does your chosen model tell you anything about independence between income mid job satisfaction? Explain why or why not.
(iv) Perform a goodness of fit test of your ordinal model. What are the degrees of freedom of the test statistic and why?
(d) Present a table with the fitted counts from 1) the independence model, 2) the ordinal model, and 3) the saturated model
(e) Given all of the analyses you have nut do you think that income and job satisfaction are independent? Why or why not.