Friday, March 10, 2006

st: Wald Chi-Square in Logistic with Cluster Option

I ran a logistic regression with a cluster option. In one model, the results showed a Wald Chi-Square in the order of 100,000. When I ran a different model (by adding additional independent variables), I got a much smaller Wald Chi-Square (in the order of 30,000 or 2,000 depending on the additional independent variable being added). I have seen a paper reporting a Wald Chi-Square as high as 30,000 in a logistic regression with a robust option, but haven't been able to locate any information about why I got such a high Wald Chi-Square. Could someone explain if my results are normal or if I have done something wrong?

Below is the partial output for three models. The three models are specified as follows:

Model 1: y is a function of 23 x's (call them x1 - x23) Model 2: y is a function of x1 - x23 in model 1 plus x24 Model 3: y is a function of x1 - x23 in model 1 plus x25

Thanks. Daniel Indro

---Model 1--- Iteration 0: log pseudolikelihood = -1413.5696 Iteration 1: log pseudolikelihood = -1348.5214 Iteration 2: log pseudolikelihood = -1313.6178 Iteration 3: log pseudolikelihood = -1302.8919 Iteration 4: log pseudolikelihood = -1301.6519 Iteration 5: log pseudolikelihood = -1301.6301 Iteration 6: log pseudolikelihood = -1301.6301

Logit estimates Number of obs = 11309 Wald chi2(23) = 113167.68 Prob > chi2 = 0.0000 Log pseudolikelihood = -1301.6301 Pseudo R2 = 0.0792

(standard errors adjusted for clustering on compid)

---Model 2--- Iteration 0: log pseudolikelihood = -1413.5696 Iteration 1: log pseudolikelihood = -1258.636 Iteration 2: log pseudolikelihood = -1226.6914 Iteration 3: log pseudolikelihood = -1220.7719 Iteration 4: log pseudolikelihood = -1219.9377 Iteration 5: log pseudolikelihood = -1219.9183 Iteration 6: log pseudolikelihood = -1219.9183

Logit estimates Number of obs = 11309 Wald chi2(24) = 32637.80 Prob > chi2 = 0.0000 Log pseudolikelihood = -1219.9183 Pseudo R2 = 0.1370

(standard errors adjusted for clustering on compid)

---Model 3--- Iteration 0: log pseudolikelihood = -1413.5696 Iteration 1: log pseudolikelihood = -1386.0868 Iteration 2: log pseudolikelihood = -1299.8042 Iteration 3: log pseudolikelihood = -1288.04 Iteration 4: log pseudolikelihood = -1286.8147 Iteration 5: log pseudolikelihood = -1286.7925 Iteration 6: log pseudolikelihood = -1286.7925

Logit estimates Number of obs = 11309 Wald chi2(24) = 1954.11 Prob > chi2 = 0.0000 Log pseudolikelihood = -1286.7925 Pseudo R2 = 0.0897

(standard errors adjusted for clustering on compid)

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