# Difference between glm and lm in R

Difference between glm and lm in R, In R, how do you tell the difference between lm and glm?

When building intervals in lm, the t-distribution is used, but in glm, the normal distribution is used.

Longer answer: The glm function fits the model via MLE, but you end up with OLS estimates due to the assumption you made about the link function (in this case normal).

## What is a glm Anova, exactly?

While maintaining all other predictors constant, a general linear model, also known as a multiple regression model, generates a t-statistic for each predictor as well as an estimate of the slope associated with the change in the outcome variable.

## When is it fair to employ a general linear model?

To see if the means of two or more groups differ, use the General Linear Model. Random factors, covariates, or a mix of crossing and nested factors can all be used.

How to find a Trimmed Mean in R » finnstats

Stepwise regression can also be used to help determine the model.

## What is the difference between glm and lm?

lm is good for models like Y = XB + e, where eNormal ( 0, s2 ). glm fits models of the type g(Y) = XB + e, where g() and e’s sample distribution must be given. The “link function” is the name given to the function ‘g.’

For fitting linear models, the computer language R provides the following functions:

**1. lm — This function is used to fit linear models.**

The syntax for this function is as follows:

lm(formula, data, …)

where:

formula: The formula for the linear model (e.g. y ~ x1 + x2)

data: The name of the data frame that contains the data

**2. glm — This is a tool for fitting generalized linear models.**

The syntax for this function is as follows:

glm(formula, family=gaussian, data, …)

where:

formula: The formula for the linear model (e.g. y ~ x1 + x2)

family: To fit the model, choose a statistical family. Gaussian is the default, however, there are also binomial, Gamma, and Poisson choices.

data: The name of the data frame in which the data is stored.

The only difference between these two functions is that the glm() function includes a family argument.

**When you use lm() or glm() to fit a linear regression model, the results will be identical.**

The glm() function, on the other hand, can be used to fit more sophisticated models like:

Logistic regression (family=binomial)

Poisson regression (poisson=family)

The examples below demonstrate how to utilize the lm() and glm() functions in practice.

## Using the lm() Function in Practice

The lm() method is used to fit a linear regression model in the following code:

fit a model of multiple linear regression

model <- lm(mpg ~ disp + hp, data=mtcars)

Now we can view the model summary

summary(model)

Call: lm(formula = mpg ~ disp + hp, data = mtcars) Residuals: Min 1Q Median 3Q Max -4.7945 -2.3036 -0.8246 1.8582 6.9363 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 30.735904 1.331566 23.083 < 2e-16 *** disp -0.030346 0.007405 -4.098 0.000306 *** hp -0.024840 0.013385 -1.856 0.073679 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.127 on 29 degrees of freedom Multiple R-squared: 0.7482, Adjusted R-squared: 0.7309 F-statistic: 43.09 on 2 and 29 DF, p-value: 2.062e-09

## Using the glm() Function in Examples

Using the glm() method, the following code shows how to fit the exact same linear regression model.

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model multivariate linear regression

model <- glm(mpg ~ disp + hp, data=mtcars)

Let’s view the model summary

summary(model)

Call: glm(formula = mpg ~ disp + hp, data = mtcars) Deviance Residuals: Min 1Q Median 3Q Max -4.7945 -2.3036 -0.8246 1.8582 6.9363 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 30.735904 1.331566 23.083 < 2e-16 *** disp -0.030346 0.007405 -4.098 0.000306 *** hp -0.024840 0.013385 -1.856 0.073679 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for gaussian family taken to be 9.775636) Null deviance: 1126.05 on 31 degrees of freedom Residual deviance: 283.49 on 29 degrees of freedom AIC: 168.62 Number of Fisher Scoring iterations: 2

The coefficient estimates and standard errors of the coefficient estimates are identical to what the lm() function produces.

Note that we can also fit a logistic regression model with the glm() function by providing family=binomial as follows.

Let’s fit the logistic regression model

model <- glm(am ~ disp + hp, data=mtcars, family=binomial)

Okay, now see the model summary

summary(model)

Call: glm(formula = am ~ disp + hp, family = binomial, data = mtcars) Deviance Residuals: Min 1Q Median 3Q Max -1.9665 -0.3090 -0.0017 0.3934 1.3682 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.40342 1.36757 1.026 0.3048 disp -0.09518 0.04800 -1.983 0.0474 * hp 0.12170 0.06777 1.796 0.0725 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 43.230 on 31 degrees of freedom Residual deviance: 16.713 on 29 degrees of freedom AIC: 22.713 Number of Fisher Scoring iterations: 8

We may also fit a Poisson regression model using the glm() function by providing family=poisson as follows.

fit Poisson regression model

model <- glm(am ~ disp + hp, data=mtcars, family=poisson) summary(model)

Call: glm(formula = am ~ disp + hp, family = poisson, data = mtcars) Deviance Residuals: Min 1Q Median 3Q Max -1.1266 -0.4629 -0.2453 0.1797 1.5428 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.214255 0.593463 0.361 0.71808 disp -0.018915 0.007072 -2.674 0.00749 ** hp 0.016522 0.007163 2.307 0.02107 * ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 23.420 on 31 degrees of freedom Residual deviance: 10.526 on 29 degrees of freedom AIC: 42.526 Number of Fisher Scoring iterations: 6

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