I want to estimate regression parameters of a Cox random effects model. Let us say that I have a categorical variable with two levels, sex for example. Then coding the variable is straightforward: 0 if male and 1 if female for example. The interpretation of the regression coefficient associated to that variable is simple.
Now let us say that I have a categorical variable with three levels. If I just code the variable with 0,1,2 for the three levels (A,B and C), the estimation of the associated regression coefficient would not be what I am looking for. If I want to estimate the risks associated with each "level" wrt the other levels, how should I code the variable ?
What I have done so far:
I define three variables.
I define one variable where I code level A as 1 and the rest (levels B and C) as 0.
I define another variable where I code level B as 1 and the rest (levels A and C) as 0.
Finally, I define a variable where I code level C as 1 and the rest (levels A and B) as 0.
I then estimate the three regression parameters assocaited to the variables.
Just to be clear, I do not want to use any package such as coxph, coxme, survival, etc.
Is there an easier way to to this ?
Your description (one predictor variable that is all ones, the other two predictor variables as indicator variables for groups B and C) is exactly recapitulating the standard treatment contrasts that R uses.
If you want to construct a model matrix with treatment contrasts for a single factor f (inside a data frame d), then model.matrix(~f, data=d) will work
d <- data.frame(f=factor(c("A","B","B","C","A")))
model.matrix(~f, data=d)
Results:
(Intercept) fB fC
1 1 0 0
2 1 1 0
3 1 1 0
4 1 0 1
5 1 0 0
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$f
[1] "contr.treatment"
You can use other contrasts if you like; these will change the parameter estimates (and interpretation!) for your individual variables, but not the overall model fit. e.g.
model.matrix(~f , data=d, contrasts=list(f=contr.sum))
I'm looking to analyze the correlation between a categorical input variable and a binomial response variable, but I'm not sure how to organize my data or if I'm planning the right analysis.
Here's my data table (variables explained below):
species<-c("Aaeg","Mcin","Ctri","Crip","Calb","Tole","Cfus","Mdes","Hill","Cpat","Mabd","Edim","Tdal","Tmin","Edia","Asus","Ltri","Gmor","Sbul","Cvic","Egra","Pvar")
scavenge<-c(1,1,0,1,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0,1,1)
dung<-c(0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0)
pred<-c(0,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0)
nectar<-c(1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,0,0)
plant<-c(0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0)
blood<-c(1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0)
mushroom<-c(0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0)
loss<-c(0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0) #1 means yes, 0 means no
data<-cbind(species,scavenge,dung,pred,nectar,plant,blood,mushroom,loss)
data #check data table
data table explanation
I have individual species listed, and the next columns are their annotated feeding types. A 1 in a given column means yes, and a 0 means no. Some species have multiple feeding types, while some have only one feeding type. The response variable I am interested in is "loss," indicating loss of a trait. I'm curious to know if any of the feeding types predict or are correlated with the status of "loss."
thoughts
I wasn't sure if there was a good way to include feeding types as one categorical variable with multiple categories. I don't think I can organize it as a single variable with the types c("scavenge","dung","pred", etc...) since some species have multiple feeding types, so I split them up into separate columns and indicated their status as 1 (yes) or 0 (no). At the moment I was thinking of trying to use a log-linear analysis, but examples I find don't quite have comparable data... and I'm happy for suggestions.
Any help or pointing in the right direction is much appreciated!
There are too little samples, you have 4 loss == 0 and 18 loss == 1. You will run into problems fitting a full logistic regression (i.e including all variables). I suggest testing for association for each feeding habit using a fisher test:
library(dplyr)
library(purrr)
# function for the fisher test
FISHER <- function(x,y){
FT = fisher.test(table(x,y))
data.frame(
pvalue=FT$p.value,
oddsratio=as.numeric(FT$estimate),
lower_limit_OR = FT$conf.int[1],
upper_limit_OR = FT$conf.int[2]
)
}
# define variables to test
FEEDING <- c("scavenge","dung","pred","nectar","plant","blood","mushroom")
# we loop through and test association between each variable and "loss"
results <- data[,FEEDING] %>%
map_dfr(FISHER,y=data$loss) %>%
add_column(var=FEEDING,.before=1)
You get the results for each feeding habit:
> results
var pvalue oddsratio lower_limit_OR upper_limit_OR
1 scavenge 0.264251538 0.1817465 0.002943469 2.817560
2 dung 1.000000000 1.1582683 0.017827686 20.132849
3 pred 0.263157895 0.0000000 0.000000000 3.189217
4 nectar 0.535201640 0.0000000 0.000000000 5.503659
5 plant 0.002597403 Inf 2.780171314 Inf
6 blood 1.000000000 0.0000000 0.000000000 26.102285
7 mushroom 0.337662338 5.0498688 0.054241930 467.892765
The pvalue is p-value from fisher.test, basically with an odds ratio > 1, the variable is positively associated with loss. Of all your variables, plant is the strongest and you can check:
> table(loss,plant)
plant
loss 0 1
0 18 0
1 1 3
Almost all that are plant=1, are loss=1.. So with your current dataset, I think this is the best you can do. Should get a larger sample size to see if this still holds.
Is there a way (function) to calculate AUC value for a keras model in R on test-set?
I have searched on google but nothing shown up.
From Keras model, we can extract the predicted values as either class or probability as follows:
Probability:
[1,] 9.913518e-01 1.087829e-02
[2,] 9.990101e-01 1.216531e-03
[3,] 9.445553e-01 6.256607e-02
[4,] 9.928864e-01 6.808311e-03
[5,] 9.993126e-01 1.028240e-03
[6,] 6.075442e-01 3.926141e-01
Class:
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
Many thanks,
Ho
Generally it does not really matter what calssifier (keras or not) did the prediction. All you need to estimate the AUC are two things: the predicted probabilities from some classifier and the actual category (for example, dead "yes" vs. "no"). With this data you can calculate both, True Positive Rate and False positive rate, thus you can also make a ROC plot and estimate AUC with this data. You can use
library(pROC)
roc_obj <- roc(category, prediction)
auc(roc_obj)
See here for some more explanation.
I'm not sure this will answer your needs as it depends on your data structure and keras output format, but have a look to Dismo package's function evaluate. You need to set up something like that:
library(dismo)
predictors <- stack of explaining variables
pres_test <- a subset of data used to model ##that you not use in your model for this testing purpose
backg_test <- true or random (background) absence data
model <- output of your model
AUC <- evaluate(pres_test, backg_test, model, predictors) ## you may bootstrap this step x time by randomly selecting 'pres_test' and 'backg_test' x time.
I am trying to run a fixed effects regression in R. When I run the linear model without the fixed effects factor being applied the model works just fine. But when I apply the factor - which is a numeric code for user ID, I get the following error:
Error in rep.int(c(1, numeric(n)), n - 1L) : cannot allocate vector of length 1055470143
I am not sure what the error means but I fear it may be an issue of coding the variable correctly in R.
I think this is more statistical and less programming problem for two reasons:
First, I am not sure whether you are using cross sectional data or panel data. If you using cross-sectional data it doesn't make sense to control for 30000 individuals(of course, they will add to variation).
Second, if you are using panel data, there are good package such as plm package in R that does this kind of computation.
An example:
set.seed(42)
DF <- data.frame(x=rnorm(1e5),id=factor(sample(seq_len(1e3),1e5,TRUE)))
DF$y <- 100*DF$x + 5 + rnorm(1e5,sd=0.01) + as.numeric(DF$id)^2
fit <- lm(y~x+id,data=DF)
This needs almost 2.5 GB RAM for the R session (if you add RAM needed by the OS this is more than many PCs have available) and takes some time to finish. The result is pretty useless.
If you don't run into RAM limitations you can suffer from limitations of vector length (e.g., if you have even more factor levels), in particular if you use an older version of R.
What happens?
One of the first steps in lm is creating the design matrix using the function model.matrix. Here is a smaller example of what happens with factors:
model.matrix(b~a,data=data.frame(a=factor(1:5),b=2))
# (Intercept) a2 a3 a4 a5
# 1 1 0 0 0 0
# 2 1 1 0 0 0
# 3 1 0 1 0 0
# 4 1 0 0 1 0
# 5 1 0 0 0 1
# attr(,"assign")
# [1] 0 1 1 1 1
# attr(,"contrasts")
# attr(,"contrasts")$a
# [1] "contr.treatment"
See how n factor levels result in n-1 dummy variables? If you have many factor levels and many observations, this matrix gets huge.
What should you do?
I'm quite sure, you should use a mixed effects model. There are two important packages that implement linear mixed effects models in R, package nlme and the newer package lme4.
library(lme4)
fit.mixed <- lmer(y~x+(1|id),data=DF)
summary(fit.mixed)
Linear mixed model fit by REML
Formula: y ~ x + (1 | id)
Data: DF
AIC BIC logLik deviance REMLdev
1025277 1025315 -512634 1025282 1025269
Random effects:
Groups Name Variance Std.Dev.
id (Intercept) 8.9057e+08 29842.472
Residual 1.3875e+03 37.249
Number of obs: 100000, groups: id, 1000
Fixed effects:
Estimate Std. Error t value
(Intercept) 3.338e+05 9.437e+02 353.8
x 1.000e+02 1.180e-01 847.3
Correlation of Fixed Effects:
(Intr)
x 0.000
This needs very little RAM, calculates fast, and is a more correct model.
See how the random intercept accounts for most of the variance?
So, you need to study mixed effects models. There are some nice publications, e.g. Baayen, Davidson, Bates (2008), explaining how to use lme4.