HOWTO compare univariate binomial glm lrm models which are not nested
Compare them by `goodness for purpose': you have not told us the purpose. Please do read some of the extensive literature on model comparison.
On Sat, 16 Apr 2005, Jan Verbesselt wrote:
Thanks a lot for the input! I forgot to add family=binomial, for a binomial glm. Now the AIC's are positive! I was planning to use AIC (from the binomial glm) and c-index (lrm) to compare and rank different uni-variate (one continue explanatory variable) logistic models to evaluate the 'performance' of the different explanatory variables in the different models. What is the best technique to compare these lrm.models, which are not nested? I found in literature that ranking based on different parameters (goodness of fit and predictability) that these can be used to compare uni-variate models. Thanks in advance, Regards, Jan-
_______________________________________________________________________ ir. Jan Verbesselt Research Associate Lab of Geomatics Engineering K.U. Leuven Vital Decosterstraat 102. B-3000 Leuven Belgium Tel: +32-16-329750 Fax: +32-16-329760 http://gloveg.kuleuven.ac.be/ _______________________________________________________________________ -----Original Message----- From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] Sent: Friday, April 15, 2005 5:06 PM To: Jan Verbesselt Cc: r-help at stat.math.ethz.ch Subject: Re: [R] negetative AIC values: How to compare models with negative AIC's AICs (like log-likelihoods) can be positive or negative. However, you fitted a Gaussian and not a binomial glm (as lrm does if m.arson is binary). For a discrete response with the usual dominating measure (counting measure) the log-likelihood is negative and hence the AIC is positive, but not in general (and it is matter of convention even there). In any case, Akaike only suggested comparing AIC for nested models, no one suggests comparing continuous and discrete models. On Fri, 15 Apr 2005, Jan Verbesselt wrote: Dear, When fitting the following model knots <- 5 lrm.NDWI <- lrm(m.arson ~ rcs(NDWI,knots) I obtain the following result: Logistic Regression Model lrm(formula = m.arson ~ rcs(NDWI, knots)) Frequencies of Responses 0 1 666 35 Obs Max Deriv Model L.R. d.f. P C Dxy Gamma Tau-a R2 Brier 701 5e-07 34.49 4 0 0.777 0.553 0.563 0.053 0.147 0.045 Coef S.E. Wald Z P Intercept -4.627 3.188 -1.45 0.1467 NDWI 5.333 20.724 0.26 0.7969 NDWI' 6.832 74.201 0.09 0.9266 NDWI'' 10.469 183.915 0.06 0.9546 NDWI''' -190.566 254.590 -0.75 0.4541 When analysing the glm fit of the same model Call: glm(formula = m.arson ~ rcs(NDWI, knots), x = T, y = T) Coefficients: (Intercept) rcs(NDWI, knots)NDWI rcs(NDWI, knots)NDWI' rcs(NDWI, knots)NDWI'' rcs(NDWI, knots)NDWI''' 0.02067 0.08441 -0.54307 3.99550 -17.38573 Degrees of Freedom: 700 Total (i.e. Null); 696 Residual Null Deviance: 33.25 Residual Deviance: 31.76 AIC: -167.7 A negative AIC occurs! How can the negative AIC from different models be compared with each other? Is this result logical? Is the lowest AIC still correct? -- Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595