asbio (version 0.2-1)

loglik.norm.plot: Plots of log-likelihood functions

Description

Plots the normal, exponential, Poisson and binomial log likelihood functions. In particular, likelihoods for parameter estimates are calculated from the pdfs given a particular dataset. For the normal pdf a fixed value for the parameter which is not being estimated ($\mu$ or $\sigma^2$ is established using OLS. It is actually irrelevant how how the other parameter is estimated so long as it is held constant when maximizing likelihood for the parameter of interest.

Usage

loglik.norm.plot(X, parameter = c("mu", "sigma.sq"), possibilities, 
plot.density=TRUE)

loglik.pois.plot(X, possibilities)

loglik.binom.plot(X,possibilities)

loglik.exp.plot(X,possibilities, plot.density=TRUE)

Arguments

X

A vector of quantitative data. Conceptually these should be counts for the Poisson log-likelihood function and binary responses (0,1) for the binomial log likelihood function. Data elements for the exponential log likelihood function must be greater t

parameter

The parameter for which ML estimation is desired in loglik.norm.plot Specification of either "mu" or "sigma.sq" is required for the normal log likelihood function. No specification is required for exponential, Pois

possibilities

A vector containing a sequence of possible parameter estimates (the function will choose one of these as the ML estimate).

plot.density

A logical command for loglik.norm.plot and loglik.exp.plot indicating whether a second graph in which densities are plotted on the pdf should be created.

Value

• A plot of the normal, Poisson, exponential, or binomial log-likelihood function is returned.

Details

These plots are helpful in explaining the workings of ML estimation for parameters. For demonstration purposes be sure to include the estimate that you "want" to maximize log-likelihood function in the vector of possibilities, e.g.mean(X).

See Also

dnorm, dpois, dexp, dbinom

Examples

##Normal log likelihood estimation of mu.
X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
mean(X)
possibilities.mu<-seq(8,14,.01)
loglik.norm.plot(X,parameter="mu",possibilities.mu)

##Normal log likelihood estimation of sigma squared.
X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
var(X)
possibilities.var<-seq(1,1.45,.001)
loglik.norm.plot(X,parameter="sigma.sq",possibilities.var)

##Exponential log likelihood estimation of theta
X<-c(0.82,0.32,0.14,0.41,0.09,0.32,0.74,4.17,0.36,1.80,0.74,0.07,0.45,2.33,0.21,
0.79,0.29,0.75,3.45)
possibilities.exp<-seq(.7,1.3,.0001)
loglik.exp.plot(X,possibilities.exp)

##Poisson log likelihood estimation of lambda.
X<-c(1,3,4,0,2,3,4,3,5)
mean(X)
possibilities.poi<-seq(2.7,2.83,.001)
loglik.pois.plot(X,possibilities.poi)

##Binomial log likelihood estimation of p.
X<-c(1,1,0,0,0,1,0,0,0,0)
mean(X)
possibilities<-seq(.2,.4,.01)
loglik.binom.plot(X,possibilities)