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bncoxuk · ‎08-18-2011

Hi Duke, your example gives pulse pressue as being perfectly explained by systolic and diastolic: pulse pressure (= (systolic - diastolic) ) But in my data, the relationship is not that tight: not the whole variable is perfectly explained, but only one of its 4 levels. I assume the principle is the same.

bncoxuk · ‎08-17-2011

I just did an experiment. It showed that one level of a variable cannot be estimated if this level has a perfect correlation with a level of another variables. Let's see the data below: data work.data; infile datalines; input y x1 x2 @@; datalines; 0 1 2 0 1 2 0 1 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 1 0 2 2 0 2 2 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 2 0 2 2 0 2 2 0 3 3 0 3 3 0 3 2 0 3 2 0 3 1 0 3 1 0 3 1 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 3 3 1 3 2 1 3 3 1 3 2 1 3 2 1 3 3 0 4 4 0 4 4 1 4 4 1 4 4 0 3 2 0 1 2 0 1 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 1 0 2 2 0 2 2 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 2 0 2 2 0 2 2 0 3 3 0 3 3 0 3 2 0 3 2 0 3 1 0 3 1 0 3 1 1 3 1 1 3 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 3 3 1 3 2 1 3 3 1 3 2 1 3 1 1 3 3 0 4 4 0 4 4 1 4 4 1 4 4 run; You can see whenever x1=4, then x2 also eqals to 4. Let's run some logistic regression: proc logistic data=work.data; class x1 x2 /param=glm; model y=x1 x2 /aggregate scale=none; run; Results: Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 4.82E-15 0.7071 0.0000 1.0000 x1 1 1 -1.6953 1.1763 2.0770 0.1495 x1 2 1 1.4020 1.1598 1.4612 0.2267 x1 3 1 -0.4055 0.9574 0.1793 0.6719 x1 4 0 0 . . . x2 1 1 -0.0799 0.8535 0.0088 0.9254 x2 2 1 1.3451 0.8710 2.3847 0.1225 x2 3 0 0 . . . x2 4 0 0 . . . You can see the results: x2=4 is the reference group, so DF=0. But x2=3 also has DF=0. Problem! This is because x2=4 is 100% correlated with x1=4. You can say in this case x2=3 acts as the reference group, and the effect of x2=4 has been explained by the other variable x1's x1=4. Let's run a linear regression model using PROC GLM: proc glm data=work.data; class x1 x2; model y=x1 x2/solution ss3; run; quit; The results are the same as below. There is no estimate for x2=3. Standard Parameter Estimate Error t Value Pr > |t| Intercept 0.5000000000 B 0.14821413 3.37 0.0010 x1 1 0.3879750199 B 0.23428608 1.66 0.1005 x1 2 -.2299495084 B 0.22891720 -1.00 0.3173 x1 3 0.1000000000 B 0.19885012 0.50 0.6160 x1 4 0.0000000000 B . . . x2 1 -.0381211799 B 0.16953676 -0.22 0.8225 x2 2 -.2618788201 B 0.16953676 -1.54 0.1252 x2 3 0.0000000000 B . . . x2 4 0.0000000000 B . . . If you change the data so that x1=4 and x2=4 are not perfectly related, then the problem disappeared. I think the explanation can be that 'the effects of the levels can only be estimated unless they have unique contribution, i.e. they are not perfectly explained by other variables'. Any better thoughts, statistically?

bncoxuk · ‎08-17-2011

I just did an experiment. It showed that one level of a variable cannot be estimated if this level has a perfect correlation with a level of another variables. Let's see the data below: data work.data; infile datalines; input y x1 x2 @@; datalines; 0 1 2 0 1 2 0 1 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 1 0 2 2 0 2 2 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 2 0 2 2 0 2 2 0 3 3 0 3 3 0 3 2 0 3 2 0 3 1 0 3 1 0 3 1 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 3 3 1 3 2 1 3 3 1 3 2 1 3 2 1 3 3 0 4 4 0 4 4 1 4 4 1 4 4 0 3 2 0 1 2 0 1 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 1 0 2 2 0 2 2 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 2 0 2 2 0 2 2 0 2 2 0 3 3 0 3 3 0 3 2 0 3 2 0 3 1 0 3 1 0 3 1 1 3 1 1 3 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 3 3 1 3 2 1 3 3 1 3 2 1 3 1 1 3 3 0 4 4 0 4 4 1 4 4 1 4 4 run; You can see whenever x1=4, then x2 also eqals to 4. Let's run some logistic regression: proc logistic data=work.data; class x1 x2 /param=glm; model y=x1 x2 /aggregate scale=none; run; Results: Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 4.82E-15 0.7071 0.0000 1.0000 x1 1 1 -1.6953 1.1763 2.0770 0.1495 x1 2 1 1.4020 1.1598 1.4612 0.2267 x1 3 1 -0.4055 0.9574 0.1793 0.6719 x1 4 0 0 . . . x2 1 1 -0.0799 0.8535 0.0088 0.9254 x2 2 1 1.3451 0.8710 2.3847 0.1225 x2 3 0 0 . . . x2 4 0 0 . . . You can see the results: x2=4 is the reference group, so DF=0. But x2=3 also has DF=0. Problem! This is because x2=4 is 100% correlated with x1=4. You can say in this case x2=3 acts as the reference group, and the effect of x2=4 has been explained by the other variable x1's x1=4. Let's run a linear regression model using PROC GLM: proc glm data=work.data; class x1 x2; model y=x1 x2/solution ss3; run; quit; The results are the same as below. There is no estimate for x2=3. Standard Parameter Estimate Error t Value Pr > |t| Intercept 0.5000000000 B 0.14821413 3.37 0.0010 x1 1 0.3879750199 B 0.23428608 1.66 0.1005 x1 2 -.2299495084 B 0.22891720 -1.00 0.3173 x1 3 0.1000000000 B 0.19885012 0.50 0.6160 x1 4 0.0000000000 B . . . x2 1 -.0381211799 B 0.16953676 -0.22 0.8225 x2 2 -.2618788201 B 0.16953676 -1.54 0.1252 x2 3 0.0000000000 B . . . x2 4 0.0000000000 B . . . If you change the data so that x1=4 and x2=4 are not perfectly related, then the problem disappeared. I think the explanation can be that 'the effects of the levels can only be estimated unless they have unique contribution, i.e. they are not perfectly explained by other variables'.

bncoxuk · ‎08-17-2011

Hi Reeza, It is correct to have DF=0 for a category of a variable in logistic regression. This indicates that this category is the base level (reference group), and other levels are contrasting with this level. I understand there is definitely a problem here. Need a statistican.

bncoxuk · ‎08-17-2011

Hi art297, thanks for your reply. Age has 5 levels: 1, 2, 3, 4, and X. So I expect there are 4 estimates (the 5th is 0). But now there is only 3.

bncoxuk · ‎08-17-2011

I used the following LOGISTIC procedure to predict the variable group, but cannot understand the output. The output showed that both levels age='4' and age='X' have DF=0 and estimates as 0. While age=’A’ is understandably the reference group, the age=’4’ group is questionable. I checked the data using PROC FREQ and found there is so such problem as quasi-complete separation. Age and sex are not perfectly related. The only problem may be from the fact that: IF sex is gay (sex=’G’), then age is definitely unknown (age=’X’). Except this situation, there is no relationship between sex and age. I tried again by combining age=’4’ into the group of age=’3’ (i.e. age’s levels are 1, 2, 3 and X), and ran the model again. This time, the level age=’3’ has the same problem with DF=0, Estimate=0. PROC LOGISTIC DATA=work.data DESC; CLASS sex age; MODEL group=sex age /AGGREGATE SCALE=NONE; /*To model group=0 or 1*/ RUN; Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -8.5254 0.0925 8502.1673 <.0001 sex F 1 0.0686 0.0760 0.8144 0.3668 sex G 1 0.1554 0.1115 1.9435 0.1633 sex M 0 0 . . . age 1 1 0.2709 0.1690 2.5692 0.1090 age 2 1 0.0275 0.1461 0.0354 0.8507 age 3 1 -0.2961 0.1285 5.3097 0.0212 age 4 0 0 . . . age X 0 0 . . .

bncoxuk · ‎08-17-2011

Yeah, it is pretty hard to describle. I will try to think for a while. Thanks.

bncoxuk · ‎08-17-2011

There are two variables, age(1, 2, 3, 4) and income(1, 2, 3). Both are categorical. if age=4 then income is always 3. That is, these two levels are perfectly correlated. The results showed that income can be predicted nicely with estimates for level 1, 2 (level 3: 0). But for age, both levels 3 and 4 have estimates 0.000. I don't know if this caused the problem. But age and income are not 100% correlated. They are only perfectly correlated when age=4 and income=3.

bncoxuk · ‎08-17-2011

There are two variables, age(1, 2, 3, 4) and income(1, 2, 3). Both are categorical. if age=4 then income is always 3. That is, these two levels are perfectly correlated. The results showed that income can be predicted nicely with estimates for level 1, 2 (level 3: 0). But for age, both levels 3 and 4 have estimates 0.000. I don't know if this caused the problem. But age and income are not 100% correlated. They are only perfectly correlated when age=4 and income=3.

bncoxuk · ‎08-17-2011

Hi, I used the PROC LOGISTIC to run a logit model. There is an independent variable called 'age' which has the levels as 1, 2, 3, 4. By default, level=4 acts as the reference group The results showed that the parameter estimates for levels 1 and 2 are reasonable, but the estimate for level 3 is exactly 0.000 (same as level 4). I tried again by incorporating 3 into level 2, and ran the model again. But this time the estimate for level 2 also became 0. There must be some problem with the data. Why? Please help.

bncoxuk · ‎08-09-2011

trekvana, yours is a complete good answer. Thanks for the guide. I believe the choice is to test both models and see whether they significantly differ in terms of results and goodness-of-fit. If there is no big difference, then clearly cumulative model is a better choice.

bncoxuk · ‎08-09-2011

Hi Reeza, Yours is a good point. I am not interested at all to compare group 1 vs group 2. I tested and compared the two models: cumulative vs multinomial, and found the latter has a much better fit than the first one. So I decided to keep the multinomial one. Anyway, my key interest is on the comparion between group 1 and group 3 (reference group). Glad to learn and practice.

bncoxuk · ‎08-05-2011

Please allow me to give a discussion on the nomial logit models and ordinal logit models. I ran analysis for a data using both methods. But the results are pretty much different. The dependent variable has 3 categories: 1 (loss<$1000), 2 ($1000<=loss<=$10000) and 3 (loss>$10000). There is a list of variables to predict the dependent variable. Two approaches of nominal logit model and ordinal logit model are used to compare the difference of parameter estimates. The 1st approach treates the dependent variable as nominal which resulted in 12 significant varables, and the 2nd approach treates the dependent variable as ordinal which resulted in only 10 significant variables. Besides, the coefficients produced are pretty incompatible. The difference between these two approaches leads to an open questinon: which result is more trusted? Personally, I prefer the nominal approach. But this approach produces two sets of coeffcients for respectively comparing group 1 vs group 3, and group 2 vs group 3. The ordinal approach added one strict constraint that the two sets of coefficients (group 1 vs group 2 + 3, group 1 + 2 vs group 3) are equal. So it is more neat and easy for interpretation. However, it is just because of this constraint which sometimes compromised the result. Any comments?

bncoxuk · ‎08-03-2011

Thanks for your consistent help.

bncoxuk · ‎08-03-2011

Thanks for sharing good idea.

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