R help - Apr 2011 - multinom() residual deviance

Running a binary logit model on the data

df <- data.frame(y=sample(letters[1:3], 100, repl=T), 
x=rnorm(100))

reveals some residual deviance:

summary(glm(y ~ ., data=df, family=binomial("logit")))

However, running a multinomial model on that data (multinom, nnet) 
reveals a residual deviance:

summary(multinom(y ~ ., data=df))

On page 203, the MASS book says that "here the deviance is 
comparing with the model that correctly predicts each person, not 
the multinomial response for each cell of the mininal model", 
followed by and instruction how to compare with the saturated 
model.

For me as a beginner, this sounds like an important warning, 
however, I don't know what the warning exactly means and hence do 
not know what the difference between the residual deviance of the 
former (binary) and the latter (multinomial) model is.

(I need the deviances to calculate some of the pseudo R-squares 
with function pR2(), package "pscl".)

Could you give good advice?

Thanks
*S*

-- 
Sascha Vieweg, saschaview at gmail.com

The two models you fit are quite different.  The first is a binomial model
equivalent to

fm <- glm(I(y == "a") ~ x, binomial, df)

which you can check leads to the same result.  I.e. this model amalgamates
classes "b" and "c" into one.

The second is a multivariate logistic model that considers all three classes
defined by your factor y, (and has twice the number of parameters, among other
things).  The three clases, "a", "b" and "c"
remain separate in the model.

Hence the two models are not directly comparable, so why should the deviance be?

Bill Venables.
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On
Behalf Of Sascha Vieweg [saschaview at gmail.com]
Sent: 09 April 2011 01:14
To: r-help at r-project.org
Subject: [R] multinom() residual deviance

Running a binary logit model on the data

df <- data.frame(y=sample(letters[1:3], 100, repl=T),
x=rnorm(100))

reveals some residual deviance:

summary(glm(y ~ ., data=df, family=binomial("logit")))

However, running a multinomial model on that data (multinom, nnet)
reveals a residual deviance:

summary(multinom(y ~ ., data=df))

On page 203, the MASS book says that "here the deviance is
comparing with the model that correctly predicts each person, not
the multinomial response for each cell of the mininal model",
followed by and instruction how to compare with the saturated
model.

For me as a beginner, this sounds like an important warning,
however, I don't know what the warning exactly means and hence do
not know what the difference between the residual deviance of the
former (binary) and the latter (multinomial) model is.

(I need the deviances to calculate some of the pseudo R-squares
with function pR2(), package "pscl".)

Could you give good advice?

Thanks
*S*

--
Sascha Vieweg, saschaview at gmail.com

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