Stepwise regression issue

HyeWonJung

JMP의 Fit Model - Stepwise 기능을 사용하여 모델을 선택하는 동안 다음과 같은 문제가 발생했습니다.

1. 상호 작용 항이 중요하지만 주효과가 중요하지 않은 경우, 주효과는 모델에서 제외되고 상호 작용 항도 제거됩니다.
2. 상호작용이나 고차 항목이 유의미한 경우, 유의미하지 않더라도 주효과를 유지해야 한다는 것을 이해합니다.
3. P-값 임계값 외에 AIC/BIC 기준을 사용하더라도 역방향 선택 과정에서 주효과는 제거됩니다.

이러한 문제와 관련하여 여러분이 가지고 계신 해결책이나 권장 사항을 알려 주시면 감사하겠습니다.

이는 첨부된 데이터를 사용하여 1차 상호 작용 항만 있는 4가지 요인을 고려할 때 Y1에서 발생했습니다.

 

JMP 단계별 선택	6번째 단계

상호작용 항인 요인 1 * 요인 4는 여전히 유의미하지만, 요인 1은 유의미하지 않기 때문에 제거되었습니다.

JMP test table.jmp

DonMcCormack

@HyeWonJung using Combine, Restrict, No Rules and Whole Effect in models that have categorical terms with more than two levels is a good way to show what is happening. As an illustration, fit the following model using the Cars 1993 data set. Vehicle Category has five levels with the following precedence order:

1. {Van&Large&Midsize&Sporty&Compact–Small}
2. {Van–Large&Midsize&Sporty&Compact}
3. {Large&Midsize–Sporty&Compact}
4. {Large–Midsize}
5. {Sport–Compact}

This is how Stepwise builds one degree of freedom contrasts. It the same approach that Partition uses to create splits. If you run Partion with Highway Mileage as the Y and Vehicle Category as the only X, the splits will occur in exactly this order. Personally, I find that contrasts created in this fashion often lack interpretability and prefer the way Generalized Regression creates one degree of freedom contrasts based on the individual levels. I'll refer to these contrasts as C1 – C5.

Change Stopping Rule to P-value Threshold and set Prob to Enter to 0.40. Keep Direction set to Forward.

Start with No Rules. Click Step until no more terms are entered. Terms are entered in the following order:

1. Weight
2. Vehicle Category (C2) * Weight
3. Vehicle Category (C1) * Weight
4. Vehicle Category (C2)
5. Vehicle Category (C4) * Weight
6. Vehicle Category (C1)

Pretty straight forward. Find the smallest p-value regardless of precedence and keep adding until nothing outside of the model has a p-value smaller or equal to 0.4.

Click Remove All and repeat for Combine

1. Weight
2. Vehicle Category (C1) * Weight AND Vehicle Category (C1)
3. Vehicle Category (C2)
4. Vehicle Category (C4) AND Vehicle Category (C3)
5. Vehicle Category (C5)

Notice that in steps 2 and 4 two effects are added simultaneously. In each case p-values are calculated separately for both terms. In the case of step 2 the first term added is an interaction whereas in step 4 it is a contrast. Also note that Vehicle Category (C2) * Weight is missing from the model even though it was the second term added in the No Rules case. That's because when tested individual Vehicle Category (C2) was significant but Vehicle Category (C2) * Weight was not once Vehicle Category (C2) was in the model. This is Combine in action.

Now do the same for Restrict

1. Weight
2. Vehicle Category (C1)
3. Vehicle Category (C1) * Weight
4. Vehicle Category (C2)

This is similar to Combine except terms are added one at a time. The contrasts C3 and C4 were not added with Restrict because the p-value for C3 (precedent to C4) was too large to enter the model. However, Combine calculates the p-values with both C3 and C4 in the model and for C4 after C3 has been added to the model. Both of which are smaller than the 0.4 cutoff.

Finally, Whole Effects

1. Weight
2. Weight*Vehicle Category (all contrasts)

Here whole effect refers to all the contrasts in any effect and not statistical heredity. In this case, the interaction has a smaller p-value and once added to the model makes the Vehicle Category main effect p-value too large to consider.

If you did this once more with Whole Effects Respecting Heredity, the main effect would be added with the interaction at step 2.

Hope this makes sense. Let me know if you have questions.