simglm | R Documentation |
Simulate data from linear and generalized linear models. Only the first covariate truely affects the response variable with coefficient equal to lambda
.
simglm(family=c("binomial", "gaussian", "poisson","Gamma"),lambda=3,n=50,p=3)
family |
the family of the distribution. |
lambda |
size of the coefficient of the first covariate. |
n |
the sample size. |
p |
the number of covarites. |
The first covariate takes 1 in half of the observations, and 0 or -1 in the other half. When lambda
gets larger, it is supposed to easier to predict the response variable.
Returned values include yx
and beta
.
yx |
a data frame including the response |
beta |
true values of the regression coefficients. |
Dabao Zhang, Department of Statistics, Purdue University
Zhang, D. (2017). A coefficient of determination for generalized linear models. The American Statistician, 71(4): 310-316.
rsq, rsq.partial, pcor
.
# Poisson Models
sdata <- simglm(family="poisson",lambda=4)
fitf <- glm(y~x.1+x.2+x.3,family=poisson,data=sdata$yx)
rsq(fitf) # type='v'
fitr <- glm(y~x.2+x.3,family=poisson,data=sdata$yx)
rsq(fitr) # type='v'
rsq(fitr,type='kl')
rsq(fitr,type='lr')
rsq(fitr,type='n')
pcor(fitr) # type='v'
pcor(fitr,type='kl')
pcor(fitr,type='lr')
pcor(fitr,type='n')
# Gamma models with shape=100
n <- 50
sdata <- simglm(family="Gamma",lambda=4,n=n)
fitf <- glm(y~x.1+x.2+x.3,family=Gamma,data=sdata$yx)
rsq(fitf) # type='v'
rsq.partial(fitf) # type='v'
fitr <- glm(y~x.2,family=Gamma,data=sdata$yx)
rsq(fitr) # type='v'
rsq(fitr,type='kl')
rsq(fitr,type='lr')
rsq(fitr,type='n')
# Likelihood-ratio-based R-squared
y <- sdata$yx$y
yhatr <- fitr$fitted.values
fit0 <- update(fitr,.~1)
yhat0 <- fit0$fitted.values
llr <- sum(log(dgamma(y,shape=100,scale=yhatr/100)))
ll0 <- sum(log(dgamma(y,shape=100,scale=yhat0/100)))
# Likelihood-ratio-based R-squared
1-exp(-2*(llr-ll0)/n)
# Corrected likelihood-ratio-based R-squared
(1-exp(-2*(llr-ll0)/n))/(1-exp(2*ll0/n))
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