R help - Oct 2003 - simulate binary data from a logistic regression model

Hi.
How can i simulate a binary data set from a logistic 
regression model?I need to manipulate parameters and so 
obtain my set of data.
I want to show the improve in analyzing binary data 
with GLM(binomial) model instead of classical ANOVA or 
NON-MODELS procedures(relative risk-odds ratio-Pearson 
test of godness of fit...)
Can you say me what is the right function to use?
Do you know any interesting simulation in the web?

Thank you.
Michele.

You can use the followings:

lp<- -5+..... #linear predictor
y<-rbinom(length(lp), size, plogis(lp))

Note that size means your "denominator" in proportions to be
simulated. For
instance, if you want binary data use size=1.


best,
vito



----- Original Message -----
From: Michele Grassi <grassi at psico.univ.trieste.it>
To: <r-help at stat.math.ethz.ch>
Sent: Thursday, October 09, 2003 11:38 AM
Subject: [R] simulate binary data from a logistic regression model

> Hi.
> How can i simulate a binary data set from a logistic
> regression model?I need to manipulate parameters and so
> obtain my set of data.
> I want to show the improve in analyzing binary data
> with GLM(binomial) model instead of classical ANOVA or
> NON-MODELS procedures(relative risk-odds ratio-Pearson
> test of godness of fit...)
> Can you say me what is the right function to use?
> Do you know any interesting simulation in the web?
>
> Thank you.
> Michele.
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

On 9 Oct 2003 at 11:38, Michele Grassi wrote:

Here is one way of doing it:
> x <- rnorm(1000)
> beta <- 1
> p <- 1/(1+exp(-beta*x))
> o <- order(x)
> plot( x[o], p[o], ylim=c(0,1), type="l")
> y <- rbinom(1000, 1, prob=p)
> model <- glm(y ~ x , family=binomial)
> summary(model)
.
.
.
> B <- 1000 # number of simulation replications
> coefs <- matrix(0, B, 2)
> for (i in 1:B) {
+    coefs[i, ] <- coef(glm(rbinom(1000,1,prob=p) ~ x, 
family=binomial))
+ }
> hist( coefs[,1])
> hist(coefs[,2])
> plot(coefs)


Kjetil Halvorsen

Hi.
How can i simulate a binary data set from a logistic 
regression model?I need to manipulate parameters and so 
obtain my set of data.
I want to show the improve in analyzing binary data 
with GLM(binomial) model instead of classical ANOVA or 
NON-MODELS procedures(relative risk-odds ratio-Pearson 
test of godness of fit...)
Can you say me what is the right function to use?
Do you know any interesting simulation in the web?

Thank you.
Michele.

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help

On Thu, 9 Oct 2003 11:38:20 +0200 (MEST)
Michele Grassi <grassi at psico.univ.trieste.it> wrote:
> Hi.
> How can i simulate a binary data set from a logistic 
> regression model?I need to manipulate parameters and so 
> obtain my set of data.
> I want to show the improve in analyzing binary data 
> with GLM(binomial) model instead of classical ANOVA or 
> NON-MODELS procedures(relative risk-odds ratio-Pearson 
> test of godness of fit...)
> Can you say me what is the right function to use?
> Do you know any interesting simulation in the web?
> 
> Thank you.
> Michele.
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
This is from the Overview help file from the Design package:

    n <- 1000    # define sample size
    set.seed(17) # so can reproduce the results
    treat <- factor(sample(c('a','b','c'), n, T))
    num.diseases <- sample(0:4, n, T)
    age <- rnorm(n, 50, 10)
    cholesterol <- rnorm(n, 200, 25)
    weight <- rnorm(n, 150, 20)
    sex <- factor(sample(c('female','male'), n, T))

    # Specify population model for log odds that Y=1
    L <- .1*(num.diseases-2) + .045*(age-50) +
      (log(cholesterol - 10)-5.2)*(-2*(treat=='a') +
          3.5*(treat=='b')+2*(treat=='c'))
    # Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)]
    y <- ifelse(runif(n) < plogis(L), 1, 0)

But note that it's no longer necessary to demonstrate that logistic
regression works better than ordinary regression when the response is binary.

---
Frank E Harrell Jr    Professor and Chair            School of Medicine
                      Department of Biostatistics    Vanderbilt University