| reduceLR {PHInfiniteEstimates} | R Documentation |
Reduce a logistic regression with monotone likelihood to a conditional regression with double descending likelihood.
Description
Reduce a logistic regression with monotone likelihood to a conditional regression with double descending likelihood.
Usage
reduceLR(Z, nvec = NULL, yvec = NULL, keep, sst = NULL, verybig = 1e+07)
Arguments
Z |
regression matrix |
nvec |
vector of sample sizes |
yvec |
vector of responses |
keep |
vector of variable names to block from consideration for removal. |
sst |
vector of sufficient statistics |
verybig |
threshold for condition number to declare colinearity. |
Details
This function implements version of Kolassa (1997). It is intended for use with extensions to multinomial regression as in Kolassa (1997) and to survival analysis as in Kolassa and Zhang (2019). The method involves linear optimization that is potentially repeated. Initial calculations were done using a proprietary coding of the simplex, in a way that allowed for later iterations to be restarted from earlier iterations; this computational advantage is not employed here, in favor of computational tools in the public domain and included in the R package lpSolve. Furthermore, Kolassa (1997) removed regressors that became linearly dependent using orthogonalization, but on further reflection this computation is unnecessary. Data in the examples are from Hirji et al. (1987), citing Goorin et al. (1987).
Value
a list with components
keepme indicators of which variables are retained in the reduced data set
moderate indicatiors of which observations are retained in the reduced data set
extreme indicators of which observations are removed in the reduced data set
toosmall indicator of whether resulting data set is too small to fit the proportional hazards regression
References
Hirji KF, Mehta CR, Patel NR (1987). “Computing Distributions for Exact Logistic Regression.” Journal of the American Statistical Association, 82(400), pp. 1110-1117. ISSN 01621459, doi:10.2307/2289388.
Goorin AM, Perez–Atayde A, Gebhardt M, Andersen J (1987). “Weekly High–Dose Methotrexate and Doxorubicin for Osteosarcoma: The Dana–Farber Cancer Institute/The Children's Hospital – Study III.” Journal of Clinical Oncology. doi:10.1200/JCO.1987.5.8.1178.
Kolassa JE (1997). “Infinite Parameter Estimates in Logistic Regression.” Scandinavian Journal of Statistics, 24, 523–530. doi:10.1111/1467-9469.00078.
Kolassa JE (2016). “Inference in the Presence of Likelihood Monotonicity for Polytomous and Logistic Regression.” Advances in Pure Mathematics, 6, 331-341. doi:10.4236/apm.2016.65024.
Kolassa JE, Zhang J (2019). https://higherlogicdownload.s3.amazonaws.com/AMSTAT/fa4dd52c-8429-41d0-abdf-0011047bfa19/UploadedImages/NCB_Conference/Presentations/2019/kolassa_toxslides.pdf. Accessed: 2019-07-14.
Examples
#Cancer Data
Z<-cbind(rep(1,8),c(rep(0,4),rep(1,4)),rep(c(0,0,1,1),2),rep(c(0,1),4))
dimnames(Z)<-list(NULL,c("1","LI","SEX","AOP"))
nvec<-c(3,2,4,1,5,5,9,17); yvec<-c(3,2,4,1,5,3,5,6)
reduceLR(Z,nvec,yvec,c("SEX","AOP"))
#CD4, CD8 data
Z<-cbind(1,c(0,0,1,1,0,0,1,0),c(0,0,0,0,1,1,0,1),c(0,0,0,0,0,1,1,0),c(0,1,0,1,0,0,0,1))
dimnames(Z)<-list(NULL,c("1","CD41","CD42","CD81","CD82"))
nvec<-c(7,1,7,2,2,13,12,3); yvec<-c(4,1,2,2,0,0,4,1)
reduceLR(Z,nvec,yvec,"CD41")