The ore.odmGLM
function builds Generalized Linear Models (GLM), which include and extend the class of linear models (linear regression). Generalized linear models relax the restrictions on linear models, which are often violated in practice. For example, binary (yes/no or 0/1) responses do not have same variance across classes.
The Oracle Data Mining GLM is a parametric modeling technique. Parametric models make assumptions about the distribution of the data. When the assumptions are met, parametric models can be more efficient than non-parametric models.
The challenge in developing models of this type involves assessing the extent to which the assumptions are met. For this reason, quality diagnostics are key to developing quality parametric models.
In addition to the classical weighted least squares estimation for linear regression and iteratively re-weighted least squares estimation for logistic regression, both solved through Cholesky decomposition and matrix inversion, Oracle Data Mining GLM provides a conjugate gradient-based optimization algorithm that does not require matrix inversion and is very well suited to high-dimensional data. The choice of algorithm is handled internally and is transparent to the user.
GLM can be used to build classification or regression models as follows:
Classification: Binary logistic regression is the GLM classification algorithm. The algorithm uses the logit link function and the binomial variance function.
Regression: Linear regression is the GLM regression algorithm. The algorithm assumes no target transformation and constant variance over the range of target values.
The ore.odmGLM
function allows you to build two different types of models. Some arguments apply to classification models only and some to regression models only.
For information on the ore.odmGLM
function arguments, invoke help(ore.odmGLM)
.
The following examples build several models using GLM. The input ore.frame
objects are R data sets pushed to the database.
Example 4-11 Building a Linear Regression Model
This example builds a linear regression model using the longley
data set.
longley_of <- ore.push(longley) longfit1 <- ore.odmGLM(Employed ~ ., data = longley_of) summary(longfit1)Listing for Example 4-11
R> longley_of <- ore.push(longley) R> longfit1 <- ore.odmGLM(Employed ~ ., data = longley_of) R> summary(longfit1) Call: ore.odmGLM(formula = Employed ~ ., data = longely_of) Residuals: Min 1Q Median 3Q Max -0.41011 -0.15767 -0.02816 0.10155 0.45539 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.482e+03 8.904e+02 -3.911 0.003560 ** GNP.deflator 1.506e-02 8.492e-02 0.177 0.863141 GNP -3.582e-02 3.349e-02 -1.070 0.312681 Unemployed -2.020e-02 4.884e-03 -4.136 0.002535 ** Armed.Forces -1.033e-02 2.143e-03 -4.822 0.000944 *** Population -5.110e-02 2.261e-01 -0.226 0.826212 Year 1.829e+00 4.555e-01 4.016 0.003037 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.3049 on 9 degrees of freedom Multiple R-squared: 0.9955, Adjusted R-squared: 0.9925 F-statistic: 330.3 on 6 and 9 DF, p-value: 4.984e-10
Example 4-12 Using Ridge Estimation for the Coefficients of the ore.odmGLM Model
This example uses the longley_of
ore.frame
from Example 4-11. Example 4-12 invokes the ore.odmGLM
function and specifies using ridge estimation for the coefficients.
longfit2 <- ore.odmGLM(Employed ~ ., data = longley_of, ridge = TRUE, ridge.vif = TRUE) summary(longfit2)Listing for Example 4-12
R> longfit2 <- ore.odmGLM(Employed ~ ., data = longley_of, ridge = TRUE, + ridge.vif = TRUE) R> summary(longfit2) Call: ore.odmGLM(formula = Employed ~ ., data = longley_of, ridge = TRUE, ridge.vif = TRUE) Residuals: Min 1Q Median 3Q Max -0.4100 -0.1579 -0.0271 0.1017 0.4575 Coefficients: Estimate VIF (Intercept) -3.466e+03 0.000 GNP.deflator 1.479e-02 0.077 GNP -3.535e-02 0.012 Unemployed -2.013e-02 0.000 Armed.Forces -1.031e-02 0.000 Population -5.262e-02 0.548 Year 1.821e+00 2.212 Residual standard error: 0.3049 on 9 degrees of freedom Multiple R-squared: 0.9955, Adjusted R-squared: 0.9925 F-statistic: 330.2 on 6 and 9 DF, p-value: 4.986e-10
Example 4-13 Building a Logistic Regression GLM
This example builds a logistic regression (classification) model. It uses the infert
data set. The example invokes the ore.odmGLM
function and specifies logistic
as the type
argument, which builds a binomial GLM.
infert_of <- ore.push(infert) infit1 <- ore.odmGLM(case ~ age+parity+education+spontaneous+induced, data = infert_of, type = "logistic") infit1Listing for Example 4-13
R> infert_of <- ore.push(infert) R> infit1 <- ore.odmGLM(case ~ age+parity+education+spontaneous+induced, + data = infert_of, type = "logistic") R> infit1 Response: case == "1" Call: ore.odmGLM(formula = case ~ age + parity + education + spontaneous + induced, data = infert_of, type = "logistic") Coefficients: (Intercept) age parity education0-5yrs education12+ yrs spontaneous induced -2.19348 0.03958 -0.82828 1.04424 -0.35896 2.04590 1.28876 Degrees of Freedom: 247 Total (i.e. Null); 241 Residual Null Deviance: 316.2 Residual Deviance: 257.8 AIC: 271.8
Example 4-14 Specifying a Reference Value in Building a Logistic Regression GLM
This example builds a logistic regression (classification) model and specifies a reference value. The example uses the infert_of
ore.frame
from Example 4-13.
infit2 <- ore.odmGLM(case ~ age+parity+education+spontaneous+induced, data = infert_of, type = "logistic", reference = 1) infit2Listing for Example 4-14
infit2 <- ore.odmGLM(case ~ age+parity+education+spontaneous+induced, data = infert_of, type = "logistic", reference = 1) infit2 Response: case == "0" Call: ore.odmGLM(formula = case ~ age + parity + education + spontaneous + induced, data = infert_of, type = "logistic", reference = 1) Coefficients: (Intercept) age parity education0-5yrs education12+ yrs spontaneous induced 2.19348 -0.03958 0.82828 -1.04424 0.35896 -2.04590 -1.28876 Degrees of Freedom: 247 Total (i.e. Null); 241 Residual Null Deviance: 316.2 Residual Deviance: 257.8 AIC: 271.8