4.1.4 Build a Generalized Linear Model

The ore.glm functions fits generalized linear models on data in an ore.frame object..

The function uses a Fisher scoring iteratively reweighted least squares (IRLS) algorithm. Instead of the traditional step of halving to prevent the selection of less optimal coefficient estimates, ore.glm uses a line search to select new coefficient estimates at each iteration, starting from the current coefficient estimates and moving through the Fisher scoring suggested estimates using the formula (1 - alpha) * old + alpha * suggested where alpha in [0, 2]. When the interp control argument is TRUE, the deviance is approximated by a cubic spline interpolation. When it is FALSE, the deviance is calculated using a follow-up data scan.

Each iteration consists of two or three embedded R execution map/reduce operations: an IRLS operation, an initial line search operation, and, if interp = FALSE, an optional follow-up line search operation. As with ore.lm, the IRLS map operation creates QR decompositions when update = "qr" or cross-products when update = "crossprod" of the model.matrix, or sparse.model.matrix if argument sparse = TRUE, and the IRLS reduce operation block updates those QR decompositions or cross-product matrices. After the algorithm has either converged or reached the maximum number of iterations, a final embedded R map/reduce operation is used to generate the complete set of model-level statistics.

The ore.glm function returns an ore.glm object.

For information on the ore.glm function arguments, call help(ore.glm).

Example 4-4 Using the ore.glm Function

This example loads the rpart package and then pushes the kyphosis data set to a temporary database table that has the proxy ore.frame object KYPHOSIS. The example builds a Generalized Linear Model using the ore.glm function and one using the glm function and calls the summary function on the models.

# Load the rpart library to get the kyphosis and solder data sets.
library(rpart)
# Logistic regression
KYPHOSIS <- ore.push(kyphosis)
kyphFit1 <- ore.glm(Kyphosis ~ ., data = KYPHOSIS, family = binomial())
kyphFit2 <- glm(Kyphosis ~ ., data = kyphosis, family = binomial())
summary(kyphFit1)
summary(kyphFit2)

Listing for Example 4-4

R> # Load the rpart library to get the kyphosis and solder data sets.
R> library(rpart)

R> # Logistic regression
R> KYPHOSIS <- ore.push(kyphosis)
R> kyphFit1 <- ore.glm(Kyphosis ~ ., data = KYPHOSIS, family = binomial())
R> kyphFit2 <- glm(Kyphosis ~ ., data = kyphosis, family = binomial())
R> summary(kyphFit1)
 
Call:
ore.glm(formula = Kyphosis ~ ., data = KYPHOSIS, family = binomial())
 
Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3124  -0.5484  -0.3632  -0.1659   2.1613  
 
Coefficients:
             Estimate Std. Error z value Pr(>|z|)   
(Intercept) -2.036934   1.449622  -1.405  0.15998   
Age          0.010930   0.006447   1.696  0.08997 . 
Number       0.410601   0.224870   1.826  0.06786 . 
Start       -0.206510   0.067700  -3.050  0.00229 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
(Dispersion parameter for binomial family taken to be 1)
 
    Null deviance: 83.234  on 80  degrees of freedom
Residual deviance: 61.380  on 77  degrees of freedom
AIC: 69.38
 
Number of Fisher Scoring iterations: 4

R> summary(kyphFit2)
 
Call:
glm(formula = Kyphosis ~ ., family = binomial(), data = kyphosis)
 
Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3124  -0.5484  -0.3632  -0.1659   2.1613  
 
Coefficients:
             Estimate Std. Error z value Pr(>|z|)   
(Intercept) -2.036934   1.449575  -1.405  0.15996   
Age          0.010930   0.006446   1.696  0.08996 . 
Number       0.410601   0.224861   1.826  0.06785 . 
Start       -0.206510   0.067699  -3.050  0.00229 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
(Dispersion parameter for binomial family taken to be 1)
 
    Null deviance: 83.234  on 80  degrees of freedom
Residual deviance: 61.380  on 77  degrees of freedom
AIC: 69.38
 
Number of Fisher Scoring iterations: 5

# Poisson regression
R> SOLDER <- ore.push(solder)
R> solFit1 <- ore.glm(skips ~ ., data = SOLDER, family = poisson())
R> solFit2 <- glm(skips ~ ., data = solder, family = poisson())
R> summary(solFit1)
 
Call:
ore.glm(formula = skips ~ ., data = SOLDER, family = poisson())
 
Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.4105  -1.0897  -0.4408   0.6406   3.7927  
 
Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.25506    0.10069 -12.465  < 2e-16 ***
OpeningM     0.25851    0.06656   3.884 0.000103 ***
OpeningS     1.89349    0.05363  35.305  < 2e-16 ***
SolderThin   1.09973    0.03864  28.465  < 2e-16 ***
MaskA3       0.42819    0.07547   5.674 1.40e-08 ***
MaskB3       1.20225    0.06697  17.953  < 2e-16 ***
MaskB6       1.86648    0.06310  29.580  < 2e-16 ***
PadTypeD6   -0.36865    0.07138  -5.164 2.41e-07 ***
PadTypeD7   -0.09844    0.06620  -1.487 0.137001    
PadTypeL4    0.26236    0.06071   4.321 1.55e-05 ***
PadTypeL6   -0.66845    0.07841  -8.525  < 2e-16 ***
PadTypeL7   -0.49021    0.07406  -6.619 3.61e-11 ***
PadTypeL8   -0.27115    0.06939  -3.907 9.33e-05 ***
PadTypeL9   -0.63645    0.07759  -8.203 2.35e-16 ***
PadTypeW4   -0.11000    0.06640  -1.657 0.097591 .  
PadTypeW9   -1.43759    0.10419 -13.798  < 2e-16 ***
Panel        0.11818    0.02056   5.749 8.97e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
(Dispersion parameter for poisson family taken to be 1)
 
    Null deviance: 6855.7  on 719  degrees of freedom
Residual deviance: 1165.4  on 703  degrees of freedom
AIC: 2781.6
 
Number of Fisher Scoring iterations: 4