Subjects in a GSS were asked their opinions about government spending on the env

Question

Subjects in a GSS were asked their opinions about government spending on the environment (E), health (H), assistance to big cities (C) , and law enforcement (L). The outcome categories are 1 - too little, 2 = about right, and 3= too much. For the homogenous association model the table shows some results, including the two-factor estimates for the EH association for coding by which estimates at category 3 of each variable equal 0.

Table 9.20 reports values when parameters sum to zero within rows and within coumns, and when parameters are zero in the first row and first column. Show how these yield the estimated EH conditional odds ratio for the too much and too little categories. Constrcut a confidence interval for that odds ratio.

I was told that the estimated odds ratio equals exp(2.142) = 8.5.. is this correct? How do you find the confidence interval from this? Thank you for your help.

EXERCISES 371 9,.19 Software Output (Based on SAS) for Fitting Model For Exercise 9.5 criteria For Assessing Goodness Of Fit Criterion Deviance Pearson Chi-Square 48 26.5224 0.5526 Log Likelihood DF Value Value/DE 48 31.6695 0.6598 1284.9404 Standard Wald 95% chi- Parameter e h e h e*h e'h DF Estimate Error Confidence Limits Square 1.0515 3.2335 14.81 0.2394 2.6049 5.55 1.66 0.26 2.1425 0.5566 1 2 1 1.4221 0.6034 2 11 0.7294 0.56670.38131.8402 0.3183 0.6211 -0.8991 1.5356 Table 9.20 Parameter Estimates for Model in Exercise 9.5 Sum to Zero Constraints Zero for First Level 0.509 0.166 -0.6760 0 0 20.065 -0.099 3-0.445 -0.068 0.163 0 0.309 1.413 0.513 0 0.720 2.142

Explanation / Answer

The confidence interval is given as

mean +- z*standardError

2.1425 +- 1.96*0.5566, for the 95% CI the value of Z is 1.96 from the Z table
solving for the plus and the minus sign, the confidence interval is given as

Lower limit = 1.05
Upper Limit = 3.23

now you can again exp this values to get the absolute value

Lower limit = exp(1.05) = 2.85
Upper Limit = exp(3.23) = 25.27

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