GLM and interactions

[John Darrington]

I'm looking at introducing interactions into the GLM command.

Following the example at 
http://ssnds.uwo.ca/statsexamples/spssanova/fdequalresults.html

The given results (which I assume to be correct) on a 2 factor analysis, with 
interactions are

source   Type III Sum of Squares        df      Mean Square     F       Sig.    

Corrected Model         210.000         5       42.000          4.755   .013    
Intercept               882.000         1       882.000         99.849  .000    
CATEGORY                 18.000         1       18.000          2.038   .1791   
DRUG                     48.000         2       24.000          2.717   .1062  
CATEGORY * DRUG         144.000         2       72.000          8.151   .0063 
Error                   106.000         12      8.833                           
 
Total                  1198.000         18                                      
 
Corrected Total         316.000         17 

Now using PSPP's current GLM implementation, without considering the 
interaction term,
we get

glm diffrate by category drug
  /intercept=include
  /design = category drug
  .


#===============#=======================#==#===========#=====#====#
#     Source    #Type III Sum of Squares|df|Mean Square|  F  |Sig.#
#===============#=======================#==#===========#=====#====#
#Corrected Model#                  66.00| 3|      22.00| 1.23| .34#
#Intercept      #                 882.00| 1|     882.00|49.39| .00#
#category       #                  18.00| 1|      18.00| 1.01| .33#
#drug           #                  48.00| 2|      24.00| 1.34| .29#
#Error          #                 250.00|14|      17.86|     |    #
#Total          #                1198.00|18|           |     |    #
#Corrected Total#                 316.00|17|           |     |    #
#===============#=======================#==#===========#=====#====#

Which looks plausible. We can see that when interactions are ignored,
the ssq gets bundled in with the error term.

Now, I thought that for purposes of the current investigation, I could
"fake" an interaction term as follows:

compute interact = drug * 10 + category.

glm diffrate by category drug interact
  /intercept=include
  /design = category drug interact
  .

My reasoning is that since all values of "category" are less than 10, 
then "interact" will have unique values for each combination of "category"
and "drug".  Obviously we'll need a more reliable way of generating
interaction terms, but this should suffice for the current purposes.

Doing this, I get:

#===============#=======================#==#===========#=====#====#
#     Source    #Type III Sum of Squares|df|Mean Square|  F  |Sig.#
#===============#=======================#==#===========#=====#====#
#Corrected Model#                 210.00| 8|      26.25| 2.23| .13#
#Intercept      #                 882.00| 1|     882.00|74.89| .00#
#category       #                    .00| 1|        .00|  .00| NaN#
#drug           #                    .00| 2|        .00|  .00|1.00#
#interact       #                 144.00| 5|      28.80| 2.45| .12#
#Error          #                 106.00| 9|      11.78|     |    #
#Total          #                1198.00|18|           |     |    #
#Corrected Total#                 316.00|17|           |     |    #
#===============#=======================#==#===========#=====#====#


which, as you can see gives the correct "interact" and Error values.
It's a bit dissapointing that the uninteracted "drug" and "category"
ssq are now zero.

So this means that to get all the sums of squares we will have to run
the get_ssq function twice - once without interactions, and once with.
And in general, for a NxN design where all the interactions are desired,
then it'll be necessary to run the function N times.

Is this a correct appraisal or am I looking at it too simplisticly?

J'



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