Slight difference in output of SAS proc genmod and R glm

Question

I am trying to reproduce a model fit using SAS proc genmod in R glm and am able to get the same estimates and SE's for all parameters except the intercept and Distance coefficient.

SAS:

    *Binomial -- pearson scale;
    proc genmod data=range.daily3;
     class ID;
      model Nr/Ne = Distance ID Distance*ID Noise_Quotient Temp_C Turbid__NTU   Sal_ppt PREC NWind EWind Time_Deployed / dist=binomial link=logit scale=p;
    run;

Analysis Of Maximum Likelihood Parameter Estimates 
Parameter   DF Estimate StandardError Wald 95% Confidence Limits Wald ChiSquare Pr > ChiSq 
Intercept   1  4.6028   0.1511        4.3067              4.8989 928.45         <.0001 
Distance    1  -0.0043  0.0001        -0.0045            -0.0040 1108.13        <.0001 
ID 1757     1  2.5452   0.1818        2.1889             2.9016  196.03         <.0001 
ID 2459     0  0.0000   0.0000        0.0000             0.0000  .              . 
Distance*ID 1  -0.0006  0.0002        -0.0010            -0.0001 5.42           0.0200 
1757  
Distance*ID 0  0.0000   0.0000        0.0000             0.0000  .              . 
2459
Noise_      1  -0.0003  0.0000        -0.0003            -0.0002 45.66          <.0001 
Quotient
Temp_C      1  -0.0425  0.0041        -0.0506            -0.0343 104.89         <.0001 
Turbid__NTU 1  -0.0209  0.0024        -0.0257            -0.0161 73.61          <.0001 
Sal_ppt     1  -0.0331  0.0188        -0.0699            0.0037  3.10           0.0783 
PREC        1  0.0058   0.0020        0.0018             0.0098  8.03           0.0046 
NWind       1  -0.0495  0.0061        -0.0613            -0.0376 66.75          <.0001 
EWind       1  0.0609   0.0084        0.0444             0.0774  52.61          <.0001 
Time_       1  -0.0041  0.0003        -0.0048            -0.0035 152.59         <.0001 
Deployed 
Scale       0  5.4044   0.0000        5.4044             5.4044     

Data was imported as .csv in R and the ID variable was converted to a factor.

longtermrange2 <- read.csv("C:/Users/Data/Ashley's Google Drive/Telemetry Data/Dissertation/Chapter1/Long-Term Range/longtermrange2.csv", sep=',',header=T, na.strings=NA)

longtermrange2$ID <- as.factor(longtermrange2$ID)

R:

quasi <- glm(cbind(Nr, Ne-Nr) ~ Noise_Quotient + Temp_C + Distance*ID + Turbid__NTU + Sal_ppt + PREC + NWind + EWind + Time_Deployed,
         ,family=quasibinomial(link=logit), data=longtermrange2)


summary(quasi, dispersion=sum(residuals(quasi,"pearson")^2)/quasi$df.residual)
    Call:
glm(formula = cbind(Nr, Ne - Nr) ~ Noise_Quotient + Temp_C + 
    Distance * ID + Turbid__NTU + Sal_ppt + PREC + NWind + EWind + 
    Time_Deployed, family = quasibinomial(link = logit), data = longtermrange2)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-20.5450   -3.4402    0.9021    3.7065   20.8752  

Coefficients:
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)      7.1480566  0.2076962  34.416  < 2e-16 ***
Noise_Quotient  -0.0002608  0.0000386  -6.757 1.40e-11 ***
Temp_C          -0.0424589  0.0041457 -10.242  < 2e-16 ***
Distance        -0.0048587  0.0002086 -23.295  < 2e-16 ***
ID2459          -2.5452458  0.1817872 -14.001  < 2e-16 ***
Turbid__NTU     -0.0209159  0.0024378  -8.580  < 2e-16 ***
Sal_ppt         -0.0330704  0.0187836  -1.761  0.07831 .  
PREC             0.0058018  0.0020478   2.833  0.00461 ** 
NWind           -0.0494535  0.0060530  -8.170 3.08e-16 ***
EWind            0.0609026  0.0083965   7.253 4.07e-13 ***
Time_Deployed   -0.0041183  0.0003334 -12.353  < 2e-16 ***
Distance:ID2459  0.0005680  0.0002440   2.327  0.01995 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasibinomial family taken to be 29.20711)

    Null deviance: 231850  on 2699  degrees of freedom
Residual deviance:  74621  on 2688  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

This Distance and Intercept estimates are the only 2 coefficients that are different, along with their standard errors.

Any idea on what could be causing this?

Answer 1

R and SAS have chosen different reference levels for the ID factor

SAS

Parameter   DF Estimate 
Intercept   1  4.6028 
ID 1757     1  2.5452   
ID 2459     0  0.0000 

R

                 Estimate  
(Intercept)      7.1480566 
ID2459          -2.5452458
ID1757           0.0

Note that R does not actually display the reference level, I've just inferred it.

Now observe that the contribution of the coefficients to the linear predictor for class 1757 is, in the SAS model

4.6028 + 2.5452 = 7.148

which is the intercept in the R model. So alltogether, the coefficients balance, and give the same predictions.

A similar thing is happening with your coefficients for the Distance*ID interaction.

SAS

Parameter       DF Estimate 
Distance        1  -0.0043
Distance*ID1757 1  -0.0006  
Distance*ID2459 0  0.0000 

R

                 Estimate  
Distance        -0.0048587  0.0002086
Distance:ID2459  0.0005680  0.0002440
Distance:ID1757  0.0

This time, observe that

-0.0043 + -0.0006 = -0.0049

which is the coefficient for Distance in the R model.