GLM in R

What is GLM in R?

GLM in R is a class of regression models that supports non-normal distributions, and can be implemented in R through glm() function that takes various parameters, and allowing user to apply various regression models like logistic, poission etc., and that the model works well with a variable which depicts a non-constant variance, with three important components viz. random, systematic, and link component making the GLM model, and R programming allowing seamless flexibility to the user in the implementation of the concept.

GLM Function

Syntax: glm (formula, family, data, weights, subset, Start=null, model=TRUE,method=””…)

Here Family types (include model types) includes binomial, Poisson, Gaussian, gamma, quasi. Each distribution performs a different usage and can be used in either classification and prediction. And when the model is gaussian, the response should be a real integer.

And when the model is binomial, the response should be classes with binary values.

And when the model is Poisson, the response should be non-negative with a numeric value.

And when the model is gamma, the response should be a positive numeric value.

glm.fit() – To fit a model

Lrfit() – denotes logistic regression fit.

update()- helps in updating a model.

anova() – its an optional test.

How to Create GLM in R?

Here we shall see how to create an easy generalized linear model with binary data using glm() function. And by continuing with Trees data set.

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Examples

// Importing a library
library(dplyr)
glimpse(trees)

To see categorical values factors are assigned.

levels(factor(trees$Girth))

// Verifying continuous variables

library(dplyr)
continuous <-select_if(trees, is.numeric)
summary(continuous)

// Including tree dataset in R search Pathattach(trees)

x<-glm(Volume~Height+Girth)
x

Output:

summary(x)

The output of the summary function gives out the calls, coefficients, and residuals. The above response figures out that both height and girth co-efficient are non-significant as the probability of them are less than 0.5. And there is two variant of deviance named null and residual. Finally, fisher scoring is an algorithm that solves maximum likelihood issues. With binomial, the response is a vector or matrix. cbind() is used to bind the column vectors in a matrix. And to get the detailed information of the fit summary is used.

To do Like hood test the following code is executed.

step(x, test="LRT")
Start:  AIC=176.91
Volume ~ Height + Girth
Df Deviance    AIC scaled dev.  Pr(>Chi)
<none>         421.9 176.91
- Height  1    524.3 181.65       6.735  0.009455 **
- Girth   1   5204.9 252.80      77.889 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Call:  glm(formula = Volume ~ Height + Girth)
Coefficients:
(Intercept)       Height        Girth
-57.9877       0.3393       4.7082
Degrees of Freedom: 30 Total (i.e. Null);  28 Residual
Null Deviance:     8106
Residual Deviance: 421.9      AIC: 176.9

Model fit

a<-cbind(Height,Girth - Height)
> a

summary(trees)

Girth           Height       Volume
Min.   : 8.30   Min.   :63   Min.   :10.20
1st Qu.:11.05   1st Qu.:72   1st Qu.:19.40
Median :12.90   Median :76   Median :24.20
Mean   :13.25   Mean   :76   Mean   :30.17
3rd Qu.:15.25   3rd Qu.:80   3rd Qu.:37.30
Max.   :20.60   Max.   :87   Max.   :77.00

To get the appropriate standard deviation

apply(trees, sd)
Girth    Height    Volume
3.138139 6.371813 16.437846
predict <- predict(logit, data_test, type = 'response')

Next, we refer to the count response variable to modeled a good response fit. To calculate this, we will use the USAccDeath dataset.

Let us enter the following snippets in the R console and see how the year count and year square is performed on them.

data("USAccDeaths")
force(USAccDeaths)

// To analyze the year from 1973-1978.

disc <- data.frame(count=as.numeric(USAccDeaths),year=seq(0,(length(USAccDeaths)-1),1)))
yearSqr=disc$year^2
a1 <- glm(count~year+yearSqr,family="poisson",data=disc)
summary(a1)

To verify the best of fit of the model the following command can be used to find

the residuals for the test. From the below result the value is 0.

1 - pchisq(deviance(a1),df.residual(a1))

Using QuasiPoisson  family for the greater variance in the given data

a2 <- glm(count~year+yearSqr,family="quasipoisson",data=disc)
summary(a2)

Comparing Poisson with binomial AIC value differs significantly. They can be analyzed by precision and recall ratio. Next step is to verify residuals variance is proportional to the mean. Then we can plot using ROCR library to improve the model.

Conclusion

Therefore, we have focussed on special model called generalized linear model which helps in focussing and estimating the model parameters. It is primarily the potential for a continuous response variable. And we have seen how glm fits an R built-in packages. They are the most popular approaches for measuring count data and a robust tool for classification techniques utilized by a data scientist. R language, of course, helps in doing complicated mathematical functions

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