# logit_syn: Logistic regression : generic synthetic binary/binomial... In COUNT: Functions, Data and Code for Count Data

## Description

logit_syn is a generic function for developing synthetic logistic regression data and a model given user defined specifications.

## Usage

 `1` ```logit_syn(nobs=50000, d=1, xv = c(1, 0.5, -1.5)) ```

## Arguments

 `nobs` number of observations in model, Default is 50000 `d` binomial denominator, Default is 1, a binary logistic model. May use a variable containing different denominator values. `xv` predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

## Details

Create a synthetic logistic regression model using the appropriate arguments. Binomial denominator must be declared. For a binary logistic model, d=1. A variable may be used as the denominator when values differ. See examples.

## Value

 `by` binomial logistic numerator; number of successes `sim.data` synthetic data set

## Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

## References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press. Hilbe, J.M. (2009), Logistic Regression Models, Chapman & Hall/CRCD

`probit_syn`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```# Binary logistic regression (denominator=1) sim.data <-logit_syn(nobs = 500, d = 1, xv = c(1, .5, -1.5)) mylogit <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data) summary(mylogit) confint(mylogit) # Binary logistic regression with odds ratios (denominator=1); 3 predictors sim.data <-logit_syn(nobs = 500, d = 1, xv = c(1, .75, -1.5, 1.15)) mylogit <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data) exp(coef(mylogit)) exp(confint(mylogit)) # Binomial or grouped logistic regression with defined denominator, den den <- rep(1:5, each=100, times=1)*100 sim.data <- logit_syn(nobs = 500, d = den, xv = c(1, .5, -1.5)) gby <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data) summary(gby) ## Not run: # default sim.data <- logit_syn(nobs=500, d=1, xv = c(2, -.55, 1.15)) dlogit <- glm(cbind(by,dby) ~ . , family=binomial(link="logit"), data = sim.data) summary(dlogit) ## End(Not run) ```