[R] Residual deviance (cross-post from sci.stat.consult)

[Serebrenik, A.]

Dear all,

I'm trying to fit a statistical model to series of measurements.
Unfortunately, my knowledge of statistics is rather limited, so I'm a
bit at loss of what is going on with the model.

First of all, I've prepared a histogram. Then, I've tried to fit a Poisson model to express the relation between the middle points of
classes (mids) and the corresponding frequencies (density). I've got the following Poisson models using R:

> summary(fmDP)

Deviance Residuals:
     Min        1Q    Median        3Q       Max
-1.20831  -0.56363  -0.28010   0.08324   3.19099

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.2495     0.1528    8.18 2.84e-16 ***
hD$mids      -3.3683     0.4420   -7.62 2.53e-14 ***
---
Signif. codes:  0 ~Q***~R 0.001 ~Q**~R 0.01 ~Q*~R 0.05 ~Q.~R 0.1 ~Q ~R 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 129.59  on 99  degrees of freedom
Residual deviance:  55.67  on 98  degrees of freedom
AIC: Inf

Number of Fisher Scoring iterations: 5

> summary(fmDPAll)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-1.3687  -0.5672  -0.3386   0.0513   4.9680

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)    1.478      0.148   9.988   <2e-16 ***
hDAll$mids    -4.327      0.501  -8.636   <2e-16 ***
---
Signif. codes:  0 ~Q***~R 0.001 ~Q**~R 0.01 ~Q*~R 0.05 ~Q.~R 0.1 ~Q ~R 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 181.646  on 99  degrees of freedom
Residual deviance:  74.457  on 98  degrees of freedom
AIC: Inf

Number of Fisher Scoring iterations: 5

As 55.67 < 74.457 the first model seems to fit better than the second
one, but how good is it? Should I compare these residual deviances
with chi-square? Should I look for some other model with smaller
residual deviance?

Best regards,
Alexander