calcR2: Compute the R square using the predicted values

In bozenne/butils: Various useful functions

Compute the R square using the predicted values

Description

Compute the R square using the predicted values

Usage

calcR2(model, data = NULL, trace = FALSE)

Arguments

model	the model from which the R squared should be computed.
data	the data that have been used to fit the model.
trace	should the execution of the function be traced.

Details

Compute the Generalized R2 defined by Buse (1973) using the formula:

R^2 = 1- \frac{e S^{-1} e}{e0 S^{-1} e0}

where iS is the inverse of the variance-covariance matrix of the observations. e is the vector of residuals of the full model. e0 is the vector of residuals of the reduced model.

Compute the Generalized R2 based on the log-likelihood:

R^2 = 1 - exp(- LR / n)

where n is the number of observations. LR is twice the log of the ratio of the likelihood between the full and reduced model.

Denoting X the covariate of interest, Y the outcome, and Z the other covariates, the partial R^2 is the same as:

• the square of the partial correlation coefficient between X and Y, controlling for Z.

• the partial \eta^2 which is the ratio between the sum of squares from X (SSX) and the sum of SSX and the residual sum of squares (SSE)

References

A. Buse (1973). Goodness of Fit in Generalized Least Squares Estimation. The American Statistician,, Vol. 27, No. 3. Lonnie Magee (1990). R2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests, The American Statistician, 44:3, 250-253. https://stats.stackexchange.com/questions/64010/importance-of-predictors-in-multiple-regression-partial-r2-vs-standardized

Examples

library(lava)
library(nlme)

m <- lvm(Y~X1+X2+X3, G~1)
categorical(m, K=5, label = c("A","B","C","D","E")) <- ~G
d <- lava::sim(m, 1e2)
d <- d[order(d$G),]
d$Y <- d$Y + 0.5*as.numeric(as.factor(d$G))

## linear model
m.lm <- lm(Y~X1+X2+X3, data = d)
calcR2(m.lm)
summary(m.lm)

summary(m.lm)$r.squared

ff <- Y~X1+X2+X3
m.lm <- lm(ff, data = d)
calcR2(m.lm)
summary(m.lm)

dt <- as.data.table(d)
dt[,interaction := X1*X2]
m.lm2 <- lm(Y~X1+X2+X3+interaction, data = dt[G %in% c("A","B")])
calcR2(m.lm2)

## gls model
m.gls1 <- gls(Y~X1+X2+X3, data = d)
calcR2(m.gls1)

## heteroschedasticity
m.gls2 <- gls(Y~X1+X2+X3,
              weights = varIdent(form = ~ 1 |G), data = d)
calcR2(m.gls2)

## correlation
m.gls2 <- gls(Y~X1+X2+X3,
              correlation = corCompSymm(form = ~ 1 |G), data = d)
calcR2(m.gls2)

bozenne/butils documentation built on Oct. 14, 2023, 6:19 a.m.