predict.glm -> which class does it predict?

> Hi, 
> 
> I have a question about logistic regression in R. 
> 
> Suppose I have a small list of proteins P1, P2, P3 that predict a   
> two-class target T, say cancer/noncancer. Lets further say I know   
> that I can build a simple logistic regression model in R 
> 
> model <- glm(T ~ ., data=d.f(Y), family=binomial)   (Y is the   
> dataset of the Proteins). 
> 
> This works fine. T is a factored vector with levels cancer,   
> noncancer. Proteins are numeric. 
> 
> Now, I want to use predict.glm to predict a new data. 
> 
> predict(model, newdata=testsamples, type="response")    (testsamples   
> is a small set of new samples). 
> 
> The result is a vector of the probabilites for each sample in   
> testsamples. But probabilty WHAT for? To belong to the first level   
> in T? To belong to second level in T? 
> 
> Is this fallowing expression 
> factor(predict(model, newdata=testsamples, type="response") >= 0.5) 
> TRUE, when the new sample is classified to Cancer or when it‘s   
> classified to Noncancer? And why not the other way around? 
> 
> Thank you, 
> 
> Peter

> Hi, 
> 
> I have a question about logistic regression in R. 
> 
> Suppose I have a small list of proteins P1, P2, P3 that predict a 
> two-class target T, say cancer/noncancer. Lets further say I know that I 
> can build a simple logistic regression model in R 
> 
> model <- glm(T ~ ., data=d.f(Y), family=binomial)   (Y is the dataset of 
> the Proteins). 
> 
> This works fine. T is a factored vector with levels cancer, noncancer. 
> Proteins are numeric. 
> 
> Now, I want to use predict.glm to predict a new data. 
> 
> predict(model, newdata=testsamples, type="response")    (testsamples is 
> a small set of new samples). 
> 
> The result is a vector of the probabilites for each sample in 
> testsamples. But probabilty WHAT for? To belong to the first level in T? 
> To belong to second level in T? 
> 
> Is this fallowing expression 
> factor(predict(model, newdata=testsamples, type="response") >= 0.5) 
> TRUE, when the new sample is classified to Cancer or when it‘s 
> classified to Noncancer? And why not the other way around?

> Peter Schüffler wrote: 
>> 
>> Hi, 
>> 
>> I have a question about logistic regression in R. 
>> 
>> Suppose I have a small list of proteins P1, P2, P3 that predict a 
>> two-class target T, say cancer/noncancer. Lets further say I know that I can 
>> build a simple logistic regression model in R 
>> 
>> model <- glm(T ~ ., data=d.f(Y), family=binomial)   (Y is the dataset of 
>> the Proteins). 
>> 
>> This works fine. T is a factored vector with levels cancer, noncancer. 
>> Proteins are numeric. 
>> 
>> Now, I want to use predict.glm to predict a new data. 
>> 
>> predict(model, newdata=testsamples, type="response")    (testsamples is a 
>> small set of new samples). 
>> 
>> The result is a vector of the probabilites for each sample in testsamples. 
>> But probabilty WHAT for? To belong to the first level in T? To belong to 
>> second level in T? 
>> 
>> Is this fallowing expression 
>> factor(predict(model, newdata=testsamples, type="response") >= 0.5) 
>> TRUE, when the new sample is classified to Cancer or when it‘s classified 
>> to Noncancer? And why not the other way around? 
> 
> It‘s the probability of the 2nd level of a factor response (termed "success" 
> in the documentation, even when your modeling the probability of disease or 
> death...), just like when interpreting the logistic regression itself. 
> 
> I find it easiest to sort ut this kind of issue by experimentation in 
> simplified situations. E.g. 
> 
>> x <- sample(c("A","B"),10,replace=TRUE) 
>> x 
>  [1] "B" "A" "B" "B" "A" "B" "B" "A" "B" "A" 
>> table(x) 
> x 
> A B 
> 4 6 
> 
> (notice that the relative frequency of B is 0.6) 
> 
>> glm(x~1,binomial) 
> Error in eval(expr, envir, enclos) : y values must be 0 <= y <= 1 
> In addition: Warning message: 
> In model.matrix.default(mt, mf, contrasts) : 
>  variable ‘x‘ converted to a factor 
> 
> (OK, so it won‘t go without conversion to factor. This is a good thing.) 
> 
>> glm(factor(x)~1,binomial) 
> 
> Call:  glm(formula = factor(x) ~ 1, family = binomial) 
> 
> Coefficients: 
> (Intercept) 
>     0.4055 
> 
> Degrees of Freedom: 9 Total (i.e. Null);  9 Residual 
> Null Deviance:      13.46 
> Residual Deviance: 13.46        AIC: 15.46 
> 
> (The intercept is positive, corresponding to log odds for a probability > 
> 0.5 ; i.e.,  must be that "B": 0.4055==log(6/4)) 
> 
>> predict(glm(factor(x)~1,binomial)) 
>        1         2         3         4         5         6         7       8 
> 0.4054651 0.4054651 0.4054651 0.4054651 0.4054651 0.4054651 0.4054651 
> 0.4054651 
>        9        10 
> 0.4054651 0.4054651 
>> predict(glm(factor(x)~1,binomial),type="response") 
>  1   2   3   4   5   6   7   8   9  10 
> 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 
> 
> As for why it‘s not the other way around, well, if it had been, then you 
> could have asked the same question.... 
>