negLLP {MQMF}

negLLP -ve log-likelihood for normally distributed variables

Description

negLLP calculates the negative log-likelihood for normally distributed variables allowing for some parameters to remain fixed. It assumes the presence of a function 'funk' that will calculate predicted values of a dependent variable from a vector of independent values (logobs). By having a separate vector of parameters in 'initpar' and a vector of the indices of those parameters that will be fitted (notfixed) it is possible to fit only a subset of parameters. This is useful, for example, if generating a likelihood profile, or setting up a likelihood ratio test. With more complex models it is often a useful strategy to estimate the full number of parameters in a sequence of phases, increasing the number being estimated each time while keeping the rest fixed. 'negLLP' makes such phasing of the fitting of a model to data possible. This function can be applied directly to log-transformed data for log-normally distributed data, in which case funk would need to generate log-transformed values. But can also be applied to normally distributed data, in which case one would not log-transform the data being input to the logobs argument and funk would generated the linear-space predicted values.

The selection of which parameters to vary is simply implemented through repeatedly copying the original input values from initpar and then changing those notfixed from the varying par values

Usage

negLLP(
  pars,
  funk,
  indat,
  logobs,
  initpar = pars,
  notfixed = c(1:length(pars)),
  ...
)

Arguments

pars

a vector containing the log-transformed parameters being used in funk, plus an extra sigma which is the standard deviation of the log-normal random likelihoods in dnorm

funk

the function name that calculates the predicted values from the independent values

indat

the data.frame that contains the data used by the input funk

logobs

the log-transformed observed values for comparison with the values that the model will predict for each of the independent values

initpar

this defaults to the same as pars - using all parameters

notfixed

a vector identifying the indices of the parameters to be fitted, which also defines those that will be fixed; defaults to all parameters set to vary. If some need to be kept constant so as to generate a likelihood profile then omit their index from 'notfixed'.

...

required to allow funk to access its other parameters without having to explicitly declare them in negLL

Value

the sum of the negative log-likelihoods using a normal PDF

Examples

 data(abdat)
 param <- log(c(r= 0.42,K=9400,Binit=3400,sigma=0.05)) 
 optmod <- nlm(f=negLLP,p=param,funk=simpspm,initpar=param,
              notfixed=c(1,2,3,4),indat=abdat,logobs=log(abdat$cpue))
 outfit(optmod,backtran= TRUE) #backtran=TRUE is default anyway
  
 rval <- seq(0.325,0.45,0.0125)  # set up the test sequence
 columns <- c("r","K","Binit","sigma","-veLL")
 result <- matrix(0,nrow=11,ncol=5,dimnames=list(rval,columns))
 profest <- c(r= 0.32,K=11500,Binit=4250,sigma=0.05) # end of sequence
 for (i in 1:11) { 
   param <- log(c(rval[i],profest[2:4])) #recycle the profest values to
   parinit <- param    # improve the stability of nlm as the r value
   bestmodP <- nlm(f=negLLP,p=param,funk=simpspm,initpar=parinit, #changes
                   indat=abdat,logobs=log(abdat$cpue),notfixed=c(2:4))
   bestest <- exp(bestmodP$estimate)     
   result[i,] <- c(bestest,bestmodP$minimum)  # store each result
 }
 result   #Now you can plot -veLL againt r values for the profile
 # parset()
 # plot(result[,"r"],result[,"-veLL"],type="l",lwd=2,panel.first=grid())
 # points(result[,"r"],result[,"-veLL"],pch=16,cex=1.1)