Interaction Effects in CBC

#1
Hi All,

We have a CBC study with 8 factors (features) with following no of levels (5, 5, 4, 3, 2, 2, 2, 2). We have collected data and are in the analysis phase.

We are in the process of identifying if there are in any significant interactions present in the aggregate model before estimating individual level utilities.

We created a coded design using PROC TRANSREG and merged with the choice data.

Subsequently we ran PROC LOGISTIC on choice as dependent to evaluate significance of parameters estimates.

We have the following two questions regarding the output:

1) In the final output for logistic regression the model fit statistics (-2LogL, SC, AIC) for all models (with main effects only, with one interaction term, with several interaction terms) are similar. Does this affirm that interaction terms do not help improve the model.

2) The parameter estimates for interaction terms are significant in some measures and not significant for certain others.

For e.g. FactorA has 5 levels and FactorD has 3 levels. The coded design has following terms for interaction of FactorA with FactorD:

i) FactorA1-FactorD1 --- significant
ii) FactorA2-FactorD1 --- significant
iii) FactorA3-FactorD1 --- significant
iv) FactorA4-FactorD1 --- significant
v) FactorA1-FactorD2 --- significant
vi) FactorA2-FactorD2 --- not significant
vii) FactorA3-FactorD2 --- not significant
viii) FactorA4-FactorD2 --- not significant

How do we interpret these. Does this indicate that FactorA and FactorD interaction is significant or not.

Any help in interpreting this will be greatly appreciated

Thanks,


Below is a masked sample output from PROC LOGISTIC:


Parameter DF Estimate Error Chi-Square Pr > ChiSq

Intercept 1 -0.5026 0.0190 701.5275 <.0001
FactorA1 1 0.7253 0.0352 423.4193 <.0001
FactorA2 1 0.5140 0.0359 205.2765 <.0001
FactorA3 1 0.2451 0.0373 43.1008 <.0001
FactorA4 1 -0.4634 0.0383 146.2314 <.0001
FactorB1 1 -0.7828 0.0412 360.1774 <.0001
FactorB2 1 -0.2479 0.0382 42.1760 <.0001
FactorB3 1 0.1637 0.0361 20.5305 <.0001
FactorB4 1 0.6431 0.0402 256.1852 <.0001
FactorA1FactorD1 1 0.1079 0.0494 4.7677 0.0290
FactorA2FactorD1 1 -0.5623 0.0514 119.6579 <.0001
FactorA3FactorD1 1 -0.2993 0.0497 36.2871 <.0001
FactorA4FactorD1 1 0.2597 0.0527 24.2551 <.0001
FactorA1FactorD2 1 -0.2649 0.0524 25.5231 <.0001
FactorA2FactorD2 1 0.4663 0.0553 71.0710 <.0751
FactorA3FactorD2 1 -0.2279 0.0551 17.1179 <.0601
FactorA4FactorD2 1 0.0673 0.0571 1.3904 0.2383