# rsquared: R-squared for linear regression In piecewiseSEM: Piecewise Structural Equation Modeling

 rsquared R Documentation

## R-squared for linear regression

### Description

Returns (pseudo)-R^2 values for all linear, generalized linear, and generalized linear mixed effects models.

### Usage

```rsquared(modelList, method = NULL)
```

### Arguments

 `modelList` a regression, or a list of structural equations. `method` The method used to compute the R2 value (See Details)

### Details

For mixed models, marginal R2 considers only the variance by the fixed effects, and the conditional R2 by both the fixed and random effects.

For generalized additive models fit to gaussian distribution, the function returns ths adjusted-R2. For all other distributions, it returns the proportion of deviance explained.

For GLMs (`glm`), supported methods include:

• `mcfadden` 1 - ratio of likelihoods of full vs. null models

• `coxsnell` McFadden's R2 but raised to 2/N. Upper limit is < 1

• `nagelkerke` Adjusts Cox-Snell R2 so that upper limit = 1. The DEFAULT method

For GLMERs fit to Poisson, Gamma, and negative binomial distributions (`glmer`, `glmmPQL`, `glmer.nb`), supported methods include

• `delta` Approximates the observation variance based on second-order Taylor series expansion. Can be used with many families and link functions

• `lognormal` Observation variance is the variance of the log-normal distribution

• `trigamma` Provides most accurate estimate of the observation variance but is limited to only the log link. The DEFAULT method

For GLMERs fit to the binomial distribution (`glmer`, `glmmPQL`), supported methods include:

• `theoretical` Assumes observation variance is pi^2/3

• `delta` Approximates the observation variance as above. The DEFAULT method

### Value

Returns a `data.frame` with the response, its family and link, the method used to estimate R2, and the R2 value itself. Mixed models also return marginal and conditional R2 values.

### Author(s)

Jon Lefcheck <lefcheckj@si.edu>

### References

Nakagawa, Shinichi, Paul CD Johnson, and Holger Schielzeth. "The coefficient of determination R 2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded." Journal of the Royal Society Interface 14.134 (2017): 20170213.

### Examples

```
## Not run:
# Create data
dat <- data.frame(
ynorm = rnorm(100),
ypois = rpois(100, 100),
x1 = rnorm(100),
random = letters[1:5]
)

# Get R2 for linear model
rsquared(lm(ynorm ~ x1, dat))

# Get R2 for generalized linear model
rsquared(glm(ypois ~ x1, "poisson", dat))

# Get R2 for generalized least-squares model
rsquared(gls(ynorm ~ x1, dat))

# Get R2 for linear mixed effects model (nlme)
rsquared(nlme::lme(ynorm ~ x1, random = ~ 1 | random, dat))

# Get R2 for linear mixed effects model (lme4)
rsquared(lme4::lmer(ynorm ~ x1 + (1 | random), dat))

# Get R2 for generalized linear mixed effects model (lme4)
rsquared(lme4::glmer(ypois ~ x1 + (1 | random), family = poisson, dat))

rsquared(lme4::glmer(ypois ~ x1 + (1 | random), family = poisson, dat), method = "delta")

# Get R2 for generalized linear mixed effects model (glmmPQL)
rsquared(MASS::glmmPQL(ypois ~ x1, random = ~ 1 | random, family = poisson, dat))

# Get R2 for generalized additive models (gam)
rsquared(mgcv::gam(ynorm ~ x1, dat))

## End(Not run)

```

piecewiseSEM documentation built on March 7, 2023, 7:45 p.m.