interaction when using proc logistic for data analysis

[ZhiyingYou]

Hi all,

I have a question about interaction when using proc logistic for data analysis.   I have a binary outcome death(0/1) and two binary predictors, MIHP(0/1) and black(0/1).  I ran the following codes.  To fit a logistic model with interaction between MIHP and black, I do go with two ways as follows.  I expect to see exactly the same results in the output of the two ways, but I do not.  Can anyone explain why?

Way#1: adding MIHP|black to the right hand side of the model statement

Way#2: first creating interaction variablein interact=MIHP*black, then adding MIHP, black, and interact to the rightside of the model statement

The two ways provide excatly the same model fit statistics (AIC, SC, and -2LogL), but the MLE of the parameters are not the same.

Why this happens? Which is the correct one? Or they should be used differently?

Thanks for the help,

Zhiying

[plf515]

Can you give more detail? Possibly the data?  When I tried this on a toy example, I got the same results for both models:

data junk;

input var1  var2  DV $ count;

interact = var1*var2;

datalines;

0  0 0 100

0  0 1  50

0  1 0  25

0  1 1  75

1  0 0  100

1 0  1  10

1 1 0  10

1 1 1 90

;

proc logistic data = junk;

  model DV = var1 var2 interact;

  freq count;

run;

proc logistic data = junk;

  model DV = var1|var2;

  freq count;

run;

[PGStats]

The differences you get are most likely due to differences in parameterisations. Not the same interaction levels are estimated in both fits. Look as this simple example:

data cars;

length ab ba $4;

set sashelp.cars;

a = cylinders <= 4;

b = drivetrain = "Front";

cheap = MSRP <= 30000;

ab = cats("a",a,"b",b);

ba = cats("b",b,"a",a);

run;

title "a|b";

proc logistic data=cars;

class a b;

model cheap = a|b;

ods output parameterEstimates=a_b;

run;

title "a b ab";

proc logistic data=cars;

class a b ab;

model cheap = a b ab;

ods output parameterEstimates=ab;

run;

title "a b ba";

proc logistic data=cars;

class a b ba;

model cheap = a b ba;

ods output parameterEstimates=ba;

run;

data parmEstimates;

length model classVal0 classVal1 $4;

set a_b ab ba indsname=ds;

model = scan(ds,2,".");

where DF > 0;

run;

title "Parameter estimates for the three parameterisations";

proc print data=parmEstimates noobs; run;

Check which levels of a and b are estimated in each model.

PG