[R] Non-linear maximization function in R

[peter dalgaard]

On Oct 18, 2011, at 20:12 , aazaff wrote:

> 
> # My understanding of how this is supposed to work is that the final line of
> the HOF function:
> "sum(-dbinom(y,M,fv,log=TRUE))" is supposed to give the negative log-odds of
> that function being a good fit.
> 
>> HOF(p,x=Sample,y=Aequipecten,model=4)
> [1] 63.38763
> 
> # Notice, however, that it returns a positive value, when it is supposed to
> be negative. What does this mean? What am I doing wrong?

Not reading up on the theory. 

a: That looks like a negative log likelihood. "Log odds of being a good fit" makes no sense (to me at least).

b: Likelihoods for discrete data are probabilities, hence the log likelihood is negative and the negative log likelihood is positive.

c: You usually want to maximize the likelihood, hence minimize the negative log likelihood. 

d: Your "gaussian logistic regression" below, isn't. It's a binary logistic regression, basically doing what HOF.start does, but calculating a different set of transformed parameters. 

e: The names on the return value from HOF.start doesn't seem to match the function definition???

> #Furthermore, if I attempt a non-linear maximization on this function, I
> continue to get a positive negative log-odds and what I think are
> unreasonable looking parameter estimates. What does this mean?
> 
>> sol<-nlm(HOF,p,x=Sample,y=Aequipecten,model=4)
>> sol
> $minimum
> [1] 32.72701
> 
> $estimate
> [1] -8.751336 12.687632  8.281556
> 
> $gradient
> [1] -4.640475e-07 -5.290583e-07  5.618925e-08
> 
> $code
> [1] 1
> 
> $iterations
> [1] 16
> 
> 
> # If I compare these results to simply doing a straight gaussian logistic
> regression on the vectors I get quite a different result. I'm very confident
> that this equation is working properly. I would expect the outputs of this
> function to be roughly equivalent to the results from object "p" as seen
> above, but they don't look similar at all. I'm not sure what this means.
> 
> tBLparamsForOneSpecies <- function(theData) {
> 	x <- theData[ ,1]
> 	y <- theData[ ,2]
> 	logitReg <- glm(y ~ x + I(x^2), family=binomial)
> 	b0 <- logitReg$coefficients[1]
> 	b1 <- logitReg$coefficients[2]
> 	b2 <- logitReg$coefficients[3]
> 	opt <- (-b1)/(2*b2)
> 	tol <- 1 / sqrt(-2*b2)
> 	pmax<-1/(1+exp(b1^2/(4*b2)-b0))
> 	theParams <- cbind(opt, tol, pmax)
> 	theParams
> 	}
> 
>> theData<-cbind(Sample,Aequipecten)
>> tBLparamsForOneSpecies(theData)
>> tBLparamsForOneSpecies(theData)
>        opt       tol      pmax
> x 0.6337473 0.1468823 0.2433407
> 
> #Nor do to the coefficients look similar to p either.
> 
>> glm(Aequipecten~Sample+I(Sample^2),family=binomial)
> 
> Call:  glm(formula = Aequipecten ~ Sample + I(Sample^2), family = binomial) 
> 
> Coefficients:
>  (Intercept)       Sample  I(Sample^2)  
>       -10.44          29.37         -23.18  
> 
> Degrees of Freedom: 86 Total (i.e. Null);  84 Residual
> Null Deviance:	    73.38 
> Residual Deviance: 68.07 	AIC: 74.07 
> 
> 
> # So anyway, to sum up my problem, I'm concerned that the results of my
> function HOF and of my non-linear maximization of HOF keep giving me a
> positive log-odds. I'm not sure if this is a result of a bug in the code
> somewhere, or if I actually just don't understand what I'm doing in terms of
> the statistics. I've tried to provide as much information as possible, but I
> really don't know where or what the problem is.
> 
> Thank you for any help,
> 
> Andrew
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com