Re: [R] Questions about lrm, validate, pentrace

From: <khosoda_at_med.kobe-u.ac.jp>
Date: Sat, 30 Apr 2011 00:08:12 +0900

(11/04/29 22:09), Frank Harrell wrote:
> Yes I would select that as the final model.

Thank you for your comment. I am able to be confident about my model now.

The difference you saw is caused
> by different treatment of penalization of factor variables, related to the
> use of the sum squared differences between the estimate at one category from
> the average over all categories. I think that as long as you code it one
> way consistently and pick the penalty using that coding you are OK. But if
> the coefficients of the non-factor variables depend on how the binary
> predictor is coded, there is a bit more concern.

A lot of previous studies have demonstrated that poor outcome is more frequent in treat2 than in treat 1. So, I coded treat1 as 0, and treat2 as 1 in the first mail. Then, I came back to the original coding of treat1 and treat2 in the newer mail. According to your answer, I guess I am OK. :-)

Prof Harrell, Your book (Rregression Modeling Strategies) and many kind comments helped me a lot. Thank you very much again.

--
KH


>
> Frank
>
>
> 細田弘吉 wrote:
>>
>> Thank you for you quick reply, Prof. Harrell.
>> According to your advice, I ran pentrace using a very wide range.
>>
>> > pentrace.x6factor<- pentrace(x6factor.lrm, seq(0, 100, by=0.5))
>> > plot(pentrace.x6factor)
>>
>> I attached this figure. Then,
>>
>> > pentrace.x6factor<- pentrace(x6factor.lrm, seq(0, 10, by=0.05))
>>
>> It seems reasonable that the best penalty is 2.55.
>>
>> > x6factor.lrm.pen<- update(x6factor.lrm, penalty=2.55)
>> > cbind(coef(x6factor.lrm), coef(x6factor.lrm.pen),
>> abs(coef(x6factor.lrm)-coef(x6factor.lrm.pen)))
>> [,1] [,2] [,3]
>> Intercept -4.32434556 -3.86816460 0.456180958
>> stenosis -0.01496757 -0.01091755 0.004050025
>> T1 3.04248257 2.42443034 0.618052225
>> T2 -0.75335619 -0.57194342 0.181412767
>> procedure -1.20847252 -0.82589263 0.382579892
>> ClinicalScore 0.37623189 0.30524628 0.070985611
>>
>> > validate(x6factor.lrm, bw=F, B=200)
>> index.orig training test optimism index.corrected n
>> Dxy 0.6324 0.6849 0.5955 0.0894 0.5430 200
>> R2 0.3668 0.4220 0.3231 0.0989 0.2679 200
>> Intercept 0.0000 0.0000 -0.1924 0.1924 -0.1924 200
>> Slope 1.0000 1.0000 0.7796 0.2204 0.7796 200
>> Emax 0.0000 0.0000 0.0915 0.0915 0.0915 200
>> D 0.2716 0.3229 0.2339 0.0890 0.1826 200
>> U -0.0192 -0.0192 0.0243 -0.0436 0.0243 200
>> Q 0.2908 0.3422 0.2096 0.1325 0.1582 200
>> B 0.1272 0.1171 0.1357 -0.0186 0.1457 200
>> g 1.6328 1.9879 1.4940 0.4939 1.1389 200
>> gp 0.2367 0.2502 0.2216 0.0286 0.2080 200
>>
>>
>> > validate(x6factor.lrm.pen, bw=F, B=200)
>> index.orig training test optimism index.corrected n
>> Dxy 0.6375 0.6857 0.6024 0.0833 0.5542 200
>> R2 0.3145 0.3488 0.3267 0.0221 0.2924 200
>> Intercept 0.0000 0.0000 0.0882 -0.0882 0.0882 200
>> Slope 1.0000 1.0000 1.0923 -0.0923 1.0923 200
>> Emax 0.0000 0.0000 0.0340 0.0340 0.0340 200
>> D 0.2612 0.2571 0.2370 0.0201 0.2411 200
>> U -0.0192 -0.0192 -0.0047 -0.0145 -0.0047 200
>> Q 0.2805 0.2763 0.2417 0.0346 0.2458 200
>> B 0.1292 0.1224 0.1355 -0.0132 0.1423 200
>> g 1.2704 1.3917 1.5019 -0.1102 1.3805 200
>> gp 0.2020 0.2091 0.2229 -0.0138 0.2158 200
>>
>> In the penalized model (x6factor.lrm.pen), the apparent Dxy is 0.64, and
>> bias-corrected Dxy is 0.55. The maximum absolute error is estimated to
>> be 0.034, smaller than non-penalized model (0.0915 in x6factor.lrm) The
>> changes in slope and intercept are substantially reduced in penalized
>> model. I think overfitting is improved at least to some extent. Should I
>> select this as a final model?
>>
>> I have one more question. The "procedure" variable was defined as 0/1
>> value in the previous mail. For some graphical reason, I redefined it as
>> treat1/treat2 value. Then, the best penalty value was changed from 3.05
>> to 2.55. I guess change from numeric to factorial caused this reduction
>> in penalty. Which set up should I select?
>>
>> I appreciate your help in advance.
>>
>> --
>> KH
>>
>> (11/04/26 0:21), Frank Harrell wrote:
>>> You've done a lot of good work on this. Yes I would say you have
>>> moderate
>>> overfitting with the first model. The only thing that saved you from
>>> having
>>> severe overfitting is that there seems to be a signal present [I am
>>> assume
>>> this model is truly pre-specified and was not developed at all by looking
>>> at
>>> patterns of responses Y.]
>>>
>>> The use of backwards stepdown demonstrated much worse overfitting. This
>>> is
>>> in line with what we know about the damage of stepwise selection methods
>>> that do not incorporate shrinkage. I would throw away the stepwise
>>> regression model. You'll find that the model selected is entirely
>>> arbitrary. And you can't use the "selected" variables in any re-fit of
>>> the
>>> model, i.e., you can't use lrm pretending that the two remaining
>>> variables
>>> were pre-specified. Stepwise regression methods only seem to help. When
>>> assessed properly we see that is an illusion.
>>>
>>> You are using penalizing properly but you did not print the full table of
>>> penalties vs. effective AIC. We don't have faith that you penalized
>>> enough.
>>> I tend to run pentrace using a very wide range of possible penalties to
>>> make
>>> sure I've found the global optimum.
>>>
>>> Penalization somewhat solves the EPV problem but there is no substitute
>>> for
>>> getting more data.
>>>
>>> You can run validate specifying your final penalty as an argument.
>>>
>>> Frank
>>>
>>>
>>>
>>> 細田弘吉 wrote:
>>>>
>>>> According to the advice, I tried rms package.
>>>> Just to make sure, I have data of 104 patients (x6.df), which consists
>>>> of 5 explanatory variables and one binary outcome (poor/good) (previous
>>>> model 2 strategy). The outcome consists of 25 poor results and 79 good
>>>> results. Therefore, My events per variable (EPV) is only 5 (much less
>>>> than the rule of thumb of 10).
>>>>
>>>> My questions are about validate and pentrace in rms package.
>>>> I present some codes and results.
>>>> I appreciate anybody's help in advance.
>>>>
>>>> > x6.lrm<- lrm(outcome ~ stenosis+x1+x2+procedure+ClinicalScore,
>>>> data=x6.df, x=T, y=T)
>>>>
>>>> > x6.lrm
>>>> ...
>>>> Obs 104 LR chi2 29.24 R2 0.367 C 0.816
>>>> negative 79 d.f. 5 g 1.633 Dxy 0.632
>>>> positive 25 Pr(> chi2)<0.0001 gr 5.118 gamma 0.632
>>>> max |deriv| 1e-08 gp 0.237 tau-a 0.233
>>>> Brier 0.127
>>>>
>>>> Coef S.E. Wald Z Pr(>|Z|)
>>>> Intercept -5.5328 2.6287 -2.10 0.0353
>>>> stenosis -0.0150 0.0284 -0.53 0.5979
>>>> x1 3.0425 0.9100 3.34 0.0008
>>>> x2 -0.7534 0.4519 -1.67 0.0955
>>>> procedure 1.2085 0.5717 2.11 0.0345
>>>> ClinicalScore 0.3762 0.2287 1.65 0.0999
>>>>
>>>> It seems not too bad. Next, validation by bootstrap ...
>>>>
>>>> > validate(x6.lrm, B=200, bw=F)
>>>> index.orig training test optimism index.corrected n
>>>> Dxy 0.6324 0.6960 0.5870 0.1091 0.5233 200
>>>> R2 0.3668 0.4370 0.3154 0.1216 0.2453 200
>>>> Intercept 0.0000 0.0000 -0.2007 0.2007 -0.2007 200
>>>> Slope 1.0000 1.0000 0.7565 0.2435 0.7565 200
>>>> Emax 0.0000 0.0000 0.0999 0.0999 0.0999 200
>>>> D 0.2716 0.3368 0.2275 0.1093 0.1623 200
>>>> U -0.0192 -0.0192 0.0369 -0.0561 0.0369 200
>>>> Q 0.2908 0.3560 0.1906 0.1654 0.1254 200
>>>> B 0.1272 0.1155 0.1384 -0.0229 0.1501 200
>>>> g 1.6328 2.0740 1.4647 0.6093 1.0235 200
>>>> gp 0.2367 0.2529 0.2189 0.0341 0.2026 200
>>>>
>>>> The apparent Dxy is 0.63, and bias-corrected Dxy is 0.52. The maximum
>>>> absolute error is estimated to be 0.099. The changes in slope and
>>>> intercept are also more substantial. In all, there is evidence that I am
>>>> somewhat overfitting the data, right?.
>>>>
>>>> Furthermore, using step-down variable selection ...
>>>>
>>>> > validate(x6.lrm, B=200, bw=T)
>>>>
>>>> Backwards Step-down - Original Model
>>>>
>>>> Deleted Chi-Sq d.f. P Residual d.f. P AIC
>>>> stenosis 0.28 1 0.5979 0.28 1 0.5979 -1.72
>>>> ClinicalScore 2.60 1 0.1068 2.88 2 0.2370 -1.12
>>>> x2 2.86 1 0.0910 5.74 3 0.1252 -0.26
>>>>
>>>> Approximate Estimates after Deleting Factors
>>>>
>>>> Coef S.E. Wald Z P
>>>> Intercept -5.865 1.4136 -4.149 3.336e-05
>>>> x1 2.915 0.8685 3.357 7.889e-04
>>>> procedure 1.072 0.5590 1.918 5.508e-02
>>>>
>>>> Factors in Final Model
>>>>
>>>> [1] x1 procedure
>>>> index.orig training test optimism index.corrected n
>>>> Dxy 0.5661 0.6755 0.5559 0.1196 0.4464 200
>>>> R2 0.2876 0.4085 0.2784 0.1301 0.1575 200
>>>> Intercept 0.0000 0.0000 -0.2459 0.2459 -0.2459 200
>>>> Slope 1.0000 1.0000 0.7300 0.2700 0.7300 200
>>>> Emax 0.0000 0.0000 0.1173 0.1173 0.1173 200
>>>> D 0.2038 0.3130 0.1970 0.1160 0.0877 200
>>>> U -0.0192 -0.0192 0.0382 -0.0574 0.0382 200
>>>> Q 0.2230 0.3323 0.1589 0.1734 0.0496 200
>>>> B 0.1441 0.1192 0.1452 -0.0261 0.1702 200
>>>> g 1.2628 1.9524 1.3222 0.6302 0.6326 199
>>>> gp 0.2041 0.2430 0.2043 0.0387 0.1654 199
>>>>
>>>> If I select only two variables (x1 and procedure), bias-corrected Dxy
>>>> goes down to 0.45.
>>>>
>>>> [Question 1]
>>>> I have EPV problem. Even so, should I keep the full model (5-variable
>>>> model)? or can I use the 2-variable (x1 and procedure) model which the
>>>> validate() with step-down provides?
>>>>
>>>> [Question 2]
>>>> If I use 2-variable model, should I do
>>>> x2.lrm<- lrm(postopDWI_HI ~ T1+procedure2, data=x6.df, x=T, y=T)?
>>>> or keep the value showed above by validate function?
>>>>
>>>> Next, shrinkage ...
>>>>
>>>> > pentrace(x6.lrm, seq(0, 5.0, by=0.05))
>>>> Best penalty:
>>>> penalty df
>>>> 3.05 4.015378
>>>>
>>>> The best penalty is 3.05. So, I update it with this penalty to obtain
>>>> the corresponding penalized model:
>>>>
>>>> > x6.lrm.pen<- update(x6.lrm, penalty=3.05, x=T, y=T)
>>>> > x6.lrm.pen
>>>> .....
>>>> Penalty factors
>>>>
>>>> simple nonlinear interaction nonlinear.interaction
>>>> 3.05 3.05 3.05 3.05
>>>> Final penalty on -2 log L
>>>> [,1]
>>>> [1,] 3.8
>>>>
>>>> Obs 104 LR chi2 28.18 R2 0.313 C 0.818
>>>> negative 79 d.f. 4.015 g 1.264 Dxy 0.635
>>>> positive 25 Pr(> chi2)<0.0001 gr 3.538 gamma 0.637
>>>> max |deriv| 3e-05 gp 0.201 tau-a 0.234
>>>> Brier 0.129
>>>>
>>>> Coef S.E. Wald Z Pr(>|Z|) Penalty Scale
>>>> Intercept -4.7246 2.2429 -2.11 0.0352 0.0000
>>>> stenosis -0.0105 0.0240 -0.44 0.6621 17.8021
>>>> x1 2.3605 0.7254 3.25 0.0011 0.6054
>>>> x2 -0.5385 0.3653 -1.47 0.1404 1.2851
>>>> procedure 0.9247 0.4844 1.91 0.0563 0.8576
>>>> ClinicalScore 0.3046 0.1874 1.63 0.1041 2.4779
>>>>
>>>> Arrange the coefficients of the two models side by side, and also list
>>>> the difference between the two:
>>>>
>>>> > cbind(coef(x6.lrm), coef(x6.lrm.pen),
>>>> abs(coef(x6.lrm)-coef(x6.lrm.pen)))
>>>> [,1] [,2] [,3]
>>>> Intercept -5.53281808 -4.72464766 0.808170417
>>>> stenosis -0.01496757 -0.01050797 0.004459599
>>>> x1 3.04248257 2.36051833 0.681964238
>>>> x2 -0.75335619 -0.53854750 0.214808685
>>>> procedure 1.20847252 0.92474708 0.283725441
>>>> ClinicalScore 0.37623189 0.30457557 0.071656322
>>>>
>>>> [Question 3]
>>>> Is this penalized model the one I should present for my colleagues?
>>>> I still have EPV problem. Or is EPV problem O.K. if I use penalization?
>>>>
>>>> I am still wondering about what I can do to avoid EPV problem.
>>>> Collecting new data would be a long-time and huge work...
>>>>
>>>>
>>>> (11/04/22 1:46), khosoda_at_med.kobe-u.ac.jp wrote:
>>>>> Thank you for your comment.
>>>>> I forgot to mention that varclus and pvclust showed similar results for
>>>>> my data.
>>>>>
>>>>> BTW, I did not realize rms is a replacement for the Design package.
>>>>> I appreciate your suggestion.
>>>>> --
>>>>> KH
>>>>>
>>>>> (11/04/21 8:00), Frank Harrell wrote:
>>>>>> I think it's OK. You can also use the Hmisc package's varclus
>>>>>> function.
>>>>>> Frank
>>>>>>
>>>>>>
>>>>>> 細田弘吉 wrote:
>>>>>>>
>>>>>>> Dear Prof. Harrel,
>>>>>>>
>>>>>>> Thank you very much for your quick advice.
>>>>>>> I will try rms package.
>>>>>>>
>>>>>>> Regarding model reduction, is my model 2 method (clustering and
>>>>>>> recoding
>>>>>>> that are blinded to the outcome) permissible?
>>>>>>>
>>>>>>> Sincerely,
>>>>>>>
>>>>>>> --
>>>>>>> KH
>>>>>>>
>>>>>>> (11/04/20 22:01), Frank Harrell wrote:
>>>>>>>> Deleting variables is a bad idea unless you make that a formal part
>>>>>>>> of
>>>>>>>> the
>>>>>>>> BMA so that the attempt to delete variables is penalized for.
>>>>>>>> Instead of
>>>>>>>> BMA I recommend simple penalized maximum likelihood estimation (see
>>>>>>>> the
>>>>>>>> lrm
>>>>>>>> function in the rms package) or pre-modeling data reduction that is
>>>>>>>> blinded
>>>>>>>> to the outcome variable.
>>>>>>>> Frank
>>>>>>>>
>>>>>>>>
>>>>>>>> 細田弘吉 wrote:
>>>>>>>>>
>>>>>>>>> Hi everybody,
>>>>>>>>> I apologize for long mail in advance.
>>>>>>>>>
>>>>>>>>> I have data of 104 patients, which consists of 15 explanatory
>>>>>>>>> variables
>>>>>>>>> and one binary outcome (poor/good). The outcome consists of 25 poor
>>>>>>>>> results and 79 good results. I tried to analyze the data with
>>>>>>>>> logistic
>>>>>>>>> regression. However, the 15 variables and 25 events means events
>>>>>>>>> per
>>>>>>>>> variable (EPV) is much less than 10 (rule of thumb). Therefore, I
>>>>>>>>> used R
>>>>>>>>> package, "BMA" to perform logistic regression with BMA to avoid
>>>>>>>>> this
>>>>>>>>> problem.
>>>>>>>>>
>>>>>>>>> model 1 (full model):
>>>>>>>>> x1, x2, x3, x4 are continuous variables and others are binary data.
>>>>>>>>>
>>>>>>>>>> x16.bic.glm<- bic.glm(outcome ~ ., data=x16.df,
>>>>>>>>> glm.family="binomial", OR20, strict=FALSE)
>>>>>>>>>> summary(x16.bic.glm)
>>>>>>>>> (The output below has been cut off at the right edge to save space)
>>>>>>>>>
>>>>>>>>> 62 models were selected
>>>>>>>>> Best 5 models (cumulative posterior probability = 0.3606 ):
>>>>>>>>>
>>>>>>>>> p!=0 EV SD model 1 model2
>>>>>>>>> Intercept 100 -5.1348545 1.652424 -4.4688 -5.15
>>>>>>>>> -5.1536
>>>>>>>>> age 3.3 0.0001634 0.007258 .
>>>>>>>>> sex 4.0
>>>>>>>>> .M -0.0243145 0.220314 .
>>>>>>>>> side 10.8
>>>>>>>>> .R 0.0811227 0.301233 .
>>>>>>>>> procedure 46.9 -0.5356894 0.685148 . -1.163
>>>>>>>>> symptom 3.8 -0.0099438 0.129690 . .
>>>>>>>>> stenosis 3.4 -0.0003343 0.005254 .
>>>>>>>>> x1 3.7 -0.0061451 0.144084 .
>>>>>>>>> x2 100.0 3.1707661 0.892034 3.2221 3.11
>>>>>>>>> x3 51.3 -0.4577885 0.551466 -0.9154 .
>>>>>>>>> HT 4.6
>>>>>>>>> .positive 0.0199299 0.161769 . .
>>>>>>>>> DM 3.3
>>>>>>>>> .positive -0.0019986 0.105910 . .
>>>>>>>>> IHD 3.5
>>>>>>>>> .positive 0.0077626 0.122593 . .
>>>>>>>>> smoking 9.1
>>>>>>>>> .positive 0.0611779 0.258402 . .
>>>>>>>>> hyperlipidemia 16.0
>>>>>>>>> .positive 0.1784293 0.512058 . .
>>>>>>>>> x4 8.2 0.0607398 0.267501 . .
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> nVar 2 2
>>>>>>>>> 1 3 3
>>>>>>>>> BIC -376.9082
>>>>>>>>> -376.5588 -376.3094 -375.8468 -374.5582
>>>>>>>>> post prob 0.104
>>>>>>>>> 0.087 0.077 0.061 0.032
>>>>>>>>>
>>>>>>>>> [Question 1]
>>>>>>>>> Is it O.K to calculate odds ratio and its 95% confidence interval
>>>>>>>>> from
>>>>>>>>> "EV" (posterior distribution mean) and“SD”(posterior distribution
>>>>>>>>> standard deviation)?
>>>>>>>>> For example, 95%CI of EV of x2 can be calculated as;
>>>>>>>>>> exp(3.1707661)
>>>>>>>>> [1] 23.82573 -----> odds ratio
>>>>>>>>>> exp(3.1707661+1.96*0.892034)
>>>>>>>>> [1] 136.8866
>>>>>>>>>> exp(3.1707661-1.96*0.892034)
>>>>>>>>> [1] 4.146976
>>>>>>>>> ------------------> 95%CI (4.1 to 136.9)
>>>>>>>>> Is this O.K.?
>>>>>>>>>
>>>>>>>>> [Question 2]
>>>>>>>>> Is it permissible to delete variables with small value of "p!=0"
>>>>>>>>> and
>>>>>>>>> "EV", such as age (3.3% and 0.0001634) to reduce the number of
>>>>>>>>> explanatory variables and reconstruct new model without those
>>>>>>>>> variables
>>>>>>>>> for new session of BMA?
>>>>>>>>>
>>>>>>>>> model 2 (reduced model):
>>>>>>>>> I used R package, "pvclust", to reduce the model. The result
>>>>>>>>> suggested
>>>>>>>>> x1, x2 and x4 belonged to the same cluster, so I picked up only x2.
>>>>>>>>> Based on the subject knowledge, I made a simple unweighted sum, by
>>>>>>>>> counting the number of clinical features. For 9 features (sex,
>>>>>>>>> side,
>>>>>>>>> HT2, hyperlipidemia, DM, IHD, smoking, symptom, age), the sum
>>>>>>>>> ranges
>>>>>>>>> from 0 to 9. This score was defined as ClinicalScore. Consequently,
>>>>>>>>> I
>>>>>>>>> made up new data set (x6.df), which consists of 5 variables
>>>>>>>>> (stenosis,
>>>>>>>>> x2, x3, procedure, and ClinicalScore) and one binary outcome
>>>>>>>>> (poor/good). Then, for alternative BMA session...
>>>>>>>>>
>>>>>>>>>> BMAx6.glm<- bic.glm(postopDWI_HI ~ ., data=x6.df,
>>>>>>>>> glm.family="binomial", OR=20, strict=FALSE)
>>>>>>>>>> summary(BMAx6.glm)
>>>>>>>>> (The output below has been cut off at the right edge to save space)
>>>>>>>>> Call:
>>>>>>>>> bic.glm.formula(f = postopDWI_HI ~ ., data = x6.df, glm.family =
>>>>>>>>> "binomial", strict = FALSE, OR = 20)
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> 13 models were selected
>>>>>>>>> Best 5 models (cumulative posterior probability = 0.7626 ):
>>>>>>>>>
>>>>>>>>> p!=0 EV SD model 1 model 2
>>>>>>>>> Intercept 100 -5.6918362 1.81220 -4.4688 -6.3166
>>>>>>>>> stenosis 8.1 -0.0008417 0.00815 . .
>>>>>>>>> x2 100.0 3.0606165 0.87765 3.2221 3.1154
>>>>>>>>> x3 46.5 -0.3998864 0.52688 -0.9154 .
>>>>>>>>> procedure 49.3 0.5747013 0.70164 . 1.1631
>>>>>>>>> ClinicalScore 27.1 0.0966633 0.19645 . .
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> nVar 2 2 1
>>>>>>>>> 3 3
>>>>>>>>> BIC -376.9082 -376.5588
>>>>>>>>> -376.3094 -375.8468 -375.5025
>>>>>>>>> post prob 0.208 0.175
>>>>>>>>> 0.154 0.122 0.103
>>>>>>>>>
>>>>>>>>> [Question 3]
>>>>>>>>> Am I doing it correctly or not?
>>>>>>>>> I mean this kind of model reduction is permissible for BMA?
>>>>>>>>>
>>>>>>>>> [Question 4]
>>>>>>>>> I still have 5 variables, which violates the rule of thumb, "EPV>
>>>>>>>>> 10".
>>>>>>>>> Is it permissible to delete "stenosis" variable because of small
>>>>>>>>> value
>>>>>>>>> of "EV"? Or is it O.K. because this is BMA?
>>>>>>>>>
>>>>>>>>> Sorry for long post.
>>>>>>>>>
>>>>>>>>> I appreciate your help very much in advance.
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> KH
>>>>>>>>>
>>>>>>>>> ______________________________________________
>>>>>>>>> R-help_at_r-project.org mailing list
>>>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>>>>>> PLEASE do read the posting guide
>>>>>>>>> http://www.R-project.org/posting-guide.html
>>>>>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> -----
>>>>>>>> Frank Harrell
>>>>>>>> Department of Biostatistics, Vanderbilt University
>>>>>>>> --
>>>>>>>> View this message in context:
>>>>>>>> http://r.789695.n4.nabble.com/BMA-logistic-regression-odds-ratio-model-reduction-etc-tp3462416p3462919.html
>>>>>>>>
>>>>>>>> Sent from the R help mailing list archive at Nabble.com.
>>>>>>>>
>>>>
>>>> ______________________________________________
>>>> R-help_at_r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>
>>>
>>> -----
>>> Frank Harrell
>>> Department of Biostatistics, Vanderbilt University
>>> --
>>> View this message in context:
>>> http://r.789695.n4.nabble.com/BMA-logistic-regression-odds-ratio-model-reduction-etc-tp3462416p3473354.html
>>> Sent from the R help mailing list archive at Nabble.com.
>>>
>>> ______________________________________________
>>> R-help_at_r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>> --
>> *************************************************
>>  神戸大学大学院医学研究科 脳神経外科学分野
>>  細田 弘吉
>>  
>>  〒650-0017 神戸市中央区楠町7丁目5-1
>> Phone: 078-382-5966
>> Fax : 078-382-5979
>> E-mail address
>> Office: khosoda_at_med.kobe-u.ac.jp
>> Home : khosoda_at_venus.dti.ne.jp
>> *************************************************
>>
>> ______________________________________________
>> R-help_at_r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
> -----
> Frank Harrell
> Department of Biostatistics, Vanderbilt University
> --
> View this message in context: http://r.789695.n4.nabble.com/BMA-logistic-regression-odds-ratio-model-reduction-etc-tp3462416p3483634.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help_at_r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-- *************************************************  神戸大学大学院医学研究科 脳神経外科学分野  細田 弘吉    〒650-0017 神戸市中央区楠町7丁目5-1 Phone: 078-382-5966 Fax : 078-382-5979 E-mail address Office: khosoda_at_med.kobe-u.ac.jp Home : khosoda_at_venus.dti.ne.jp ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
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