Section author: Ravi Selker, Jonathon Love, Damian Dropmann

Linear Regression (`linReg`)

Description

Linear regression is used to explore the relationship between a continuous dependent variable, and one or more continuous and/or categorical explanatory variables. Other statistical methods, such as ANOVA and ANCOVA, are in reality just forms of linear regression.

Usage

linReg(
  data,
  dep,
  covs = NULL,
  factors = NULL,
  blocks = list(list()),
  refLevels = NULL,
  intercept = "refLevel",
  r = TRUE,
  r2 = TRUE,
  r2Adj = FALSE,
  aic = FALSE,
  bic = FALSE,
  rmse = FALSE,
  modelTest = FALSE,
  anova = FALSE,
  ci = FALSE,
  ciWidth = 95,
  stdEst = FALSE,
  ciStdEst = FALSE,
  ciWidthStdEst = 95,
  coefPlot = FALSE,
  norm = FALSE,
  qqPlot = FALSE,
  resPlots = FALSE,
  durbin = FALSE,
  collin = FALSE,
  cooks = FALSE,
  emMeans = list(list()),
  ciEmm = TRUE,
  ciWidthEmm = 95,
  emmPlots = TRUE,
  emmTables = FALSE,
  emmWeights = TRUE
)

Arguments

`data`	the data as a data frame
`dep`	the dependent variable from `data`, variable must be numeric
`covs`	the covariates from `data`
`factors`	the fixed factors from `data`
`blocks`	a list containing vectors of strings that name the predictors that are added to the model. The elements are added to the model according to their order in the list
`refLevels`	a list of lists specifying reference levels of the dependent variable and all the factors
`intercept`	`'refLevel'` (default) or `'grandMean'`, coding of the intercept. Either creates contrast so that the intercept represents the reference level or the grand mean
`r`	`TRUE` (default) or `FALSE`, provide the statistical measure `R` for the models
`r2`	`TRUE` (default) or `FALSE`, provide the statistical measure `R-squared` for the models
`r2Adj`	`TRUE` or `FALSE` (default), provide the statistical measure `adjusted R-squared` for the models
`aic`	`TRUE` or `FALSE` (default), provide Aikaike’s Information Criterion (AIC) for the models
`bic`	`TRUE` or `FALSE` (default), provide Bayesian Information Criterion (BIC) for the models
`rmse`	`TRUE` or `FALSE` (default), provide RMSE for the models
`modelTest`	`TRUE` (default) or `FALSE`, provide the model comparison between the models and the NULL model
`anova`	`TRUE` or `FALSE` (default), provide the omnibus ANOVA test for the predictors
`ci`	`TRUE` or `FALSE` (default), provide a confidence interval for the model coefficients
`ciWidth`	a number between 50 and 99.9 (default: 95) specifying the confidence interval width
`stdEst`	`TRUE` or `FALSE` (default), provide a standardized estimate for the model coefficients
`ciStdEst`	`TRUE` or `FALSE` (default), provide a confidence interval for the model coefficient standardized estimates
`ciWidthStdEst`	a number between 50 and 99.9 (default: 95) specifying the confidence interval width
`coefPlot`	`TRUE` or `FALSE` (default), provide a coefficient plot where for each predictor the estimated coefficient and confidence intervals are plotted.
`norm`	`TRUE` or `FALSE` (default), perform a Shapiro-Wilk test on the residuals
`qqPlot`	`TRUE` or `FALSE` (default), provide a Q-Q plot of residuals
`resPlots`	`TRUE` or `FALSE` (default), provide residual plots where the dependent variable and each covariate is plotted against the standardized residuals.
`durbin`	`TRUE` or `FALSE` (default), provide results of the Durbin- Watson test for autocorrelation
`collin`	`TRUE` or `FALSE` (default), provide VIF and tolerence collinearity statistics
`cooks`	`TRUE` or `FALSE` (default), provide summary statistics for the Cook’s distance
`emMeans`	a formula containing the terms to estimate marginal means for, supports up to three variables per term
`ciEmm`	`TRUE` (default) or `FALSE`, provide a confidence interval for the estimated marginal means
`ciWidthEmm`	a number between 50 and 99.9 (default: 95) specifying the confidence interval width for the estimated marginal means
`emmPlots`	`TRUE` (default) or `FALSE`, provide estimated marginal means plots
`emmTables`	`TRUE` or `FALSE` (default), provide estimated marginal means tables
`emmWeights`	`TRUE` (default) or `FALSE`, weigh each cell equally or weigh them according to the cell frequency

Output

A results object containing:

`results$modelFit`	a table
`results$modelComp`	a table
`results$models`	an array of model specific results

Tables can be converted to data frames with asDF or as.data.frame(). For example:

results$modelFit$asDF

as.data.frame(results$modelFit)

Examples

data('Prestige', package='carData')

linReg(data = Prestige, dep = income,
       covs = vars(education, prestige, women),
       blocks = list(list('education', 'prestige', 'women')))

#
#  LINEAR REGRESSION
#
#  Model Fit Measures
#  ---------------------------
#    Model    R        R²
#  ---------------------------
#        1    0.802    0.643
#  ---------------------------
#
#
#  MODEL SPECIFIC RESULTS
#
#  MODEL 1
#
#
#  Model Coefficients
#  --------------------------------------------------------
#    Predictor    Estimate    SE         t         p
#  --------------------------------------------------------
#    Intercept      -253.8    1086.16    -0.234     0.816
#    women           -50.9       8.56    -5.948    < .001
#    prestige        141.4      29.91     4.729    < .001
#    education       177.2     187.63     0.944     0.347
#  --------------------------------------------------------
#