lognlm: Multiple linear regression with log Normal errors
In logNormReg: log Normal Linear Regression

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/lognlm.R

The function fits simple multiple linear regression models with log Normals erros. Two objectives as well as two optimizing functions can be used.

1 2	lognlm(formula, data, subset, weights, na.action, y = TRUE, start, model = TRUE, lik = FALSE, opt = c("nlminb", "optim"), contrasts=NULL, ...)

`formula`	a standard R formula with response and explanatory variables (and possible offset) specifying the regression model being fitted.
`data`	an optional data frame, list or environment containing some or all the variables in the model.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`weights`	an optional vector of (positive) weights to be used in the fitting process. Currently implemented only if `lik=FALSE`.
`na.action`	a function indicating what should happen when the data contain NAs. The default is set by the `na.action` setting of `options`.
`y`	logical. If `TRUE` the response vector is returned as `y` in the fit object.
`start`	(optional) starting values of the parameter to be estimated. If `start` is missing they are computed via ordinary least squares with the intercept beta0 replaced by max(beta0,median(yi)). If `lik=TRUE` (i.e. a log Normal model is fitted), `start` refers to the regression parameters and the error standard deviation; if `lik=FALSE`, `start` does not include the starting guess for the standard deviation.
`model`	logical. If `TRUE` the model frame is returned as `model` in the fit object.
`lik`	If `TRUE` the log Normal log likelihood is optimized, otherwise the sum of squared residuals based on the logs (see Details).
`opt`	the optimization function to be used. `nlminb` appears to be more efficient, probably because it uses (unlike `optim`) also the hessian matrix (supplied in the code). However results are often indistinguishable.
`contrasts`	an optional list. See the contrasts.arg of model.matrix.default.
`...`	optional arguments passed on to the optimizing functions (`nlminb` or `optim`), (and therefore should be consistent with that).

lognlm fits simple linear regression models with log Normal errors and identity link. Actually two objectives could be used.

If lik=TRUE the usual log Normal likelihood is optimized, otherwise estimation is based on minimization of the following loss function

sum(log yi- log mui)^2

where mui=xi' beta is the mean function equal to the linear predictor (as an identity link is exploited).

A list with components

`coefficients`	the regression parameters estimate.
`loglik`	The objective function value, namely the log Normal log likelihood or the sum of the squared ‘log residuals’ (depending on `lik` option).
`s2`	the error variance estimate.
`fitted.values`	the fitted values.
`residuals`	the raw residuals on the original scale, i.e. 'observed - fitted'.
`grad`	the gradient at solution.
`hessian`	the hessian matrix at solution.
`Ehessian`	the expected hessian matrix at solution (only if `lik=FALSE`).
`convergence`	the convergence code coming from the fitter function. `0` means succefull convergence.
`call`	the matched call.
`y`	the response vector (provided that `y=TRUE` has been set).
`opt`	the employed optimizer.
`lik`	logical, indicating if the fit comes from a log Normal likelihood approach.
`xlevels`	(only where relevant) a record of the levels of the factors used in fitting.
`terms`	the terms object used.
`contrasts`	(only where relevant) the contrasts used.
`model`	if requested, i.e. `model=TRUE` has been set (the default), the model frame used.
`offset`	the (possible) offset used.

Vito M.R. Muggeo

See also print.lognlm and summary.lognlm to display results.

n=300
s=.4
set.seed(123)      #just to get reproducible results..

x<-seq(.1,10,l=n) #covariate
mu<- 10+2*x  #linear regression function
y<-rlnorm(n, log(mu)-s^2/2, s) #data..

o0<-lm(log(y)~x) #the usual but WRONG model
o<- lognlm(y~x, lik=TRUE) #fit the 'right' model by ML

plot(x,y)
lines(x, mu, lwd=2)
points(x, exp(fitted(o0)), col=2, type="l", lwd=2)
points(x, fitted(o), col=3, type="l", lwd=2)
legend("topleft", legend=c("true", "lm(log(y)~x)", "lognlm(y~x)"), 
    col=c(1,2,3), lwd=2)

#Sometimes people would estimate parameters by minimizing a least square objective 
# (i.e. by setting 'lik=FALSE', see Details), wherein data would come from 
# Y = mu * exp(eps) where eps~N(0,s)..
y1<-mu*exp(rnorm(n,0,1)) #data..
o1<-lognlm(y1~x, lik=FALSE) #set 'lik=FALSE', see Details