Logistics Reg. P-value in "Type 3 Analysis" and "Analysis of Maximum Likelihood"

[QY_Liu]

The dependent variable is Y(0,1), the independent variables are A(0,1), B(0,1,2) and C is continuous. 

Model 2.

proc logistic data=tmp descending;
class A(ref='0')/param=glm;
model Y=A C A*C/clodds=pl;;
run;

The output:

Q2. Why the p_values for Effects in Type 3 Analysis are the same as the p-values for Parameters in Analysis of Maximum Likelihood?

Thank you in advance!

[PaigeMiller]

Q1: Parameter — These are tests of each coefficient in the model. The specific null hypothesis being tested for each coefficient in the model is H0: coefficient=0. So when the p-value is less than some cutoff (usually 0.05 but you can pick other cutoffs) then the conclusion is that we reject the null hypothesis. Type III test of Effect — tests whether the effect(s) due to that term in the model is zero or not.

Q2: In the simple case where a parameter has one degree of freedom (or two levels), the Type III and maximum likelihood tests are supposed to be identical.

[QY_Liu]

Thank you, PaigeMiller.
I like to know how the chi-square statistic calculated in the two tables. Could you please suggest some reference?

[StatDave · Accepted solution]

In the Parameter Estimates table, the Wald chi-square statistic for a parameter is computed as (estimate/std.error)**2. In the Type 3 table, the statistics are computed as shown in the "Details: Testing Linear Hypotheses about the Regression Coefficients" section of the LOGISTIC documentation. When only one parameter (1 df) is involved, they are the same.

[QY_Liu]

Thank you so much!

[QY_Liu]

The dependent variable is Y(0,1), the independent variables are A(0,1), B(0,1,2) and C is continuous. 

Model 1.

proc logistic data=tmp descending;
class A(ref='0') B(ref='0')/param=glm;
model Y=A B A*B/clodds=pl;
run;

The output:

Q1. What's the hypothesis for Effect A, B and A*B in Type 3 Analysis and what's the hypothesis for Parameter A(1), B(1,2) and A*B(1*1, 1*2) in Analysis of Maximum Likelihood?

Thank you in advance!

[PaigeMiller]

duplicate question -- do not reply here -- reply at https://communities.sas.com/t5/Statistical-Procedures/Logistics-Reg-P-value-in-quot-Type-3-Analysis-...