Multivariate Regression

Fits a multivariate linear model that uses weights and variance estimates appropriate for the edsurvey.data.frame.

Usage

mvrlm.sdf(
  formula,
  data,
  weightVar = NULL,
  relevels = list(),
  jrrIMax = 1,
  dropOmittedLevels = TRUE,
  defaultConditions = TRUE,
  recode = NULL,
  returnVarEstInputs = FALSE,
  estMethod = "OLS",
  verbose = TRUE,
  omittedLevels = deprecated()
)

Arguments

formula: a Formula for the linear model. See Formula; left-hand side variables are separated with vertical pipes (|). See Examples.
data: an edsurvey.data.frame or an edsurvey.data.frame.list
weightVar: character indicating the weight variable to use (see Details). The weightVar must be one of the weights for the edsurvey.data.frame. If NULL, uses the default for the edsurvey.data.frame.
relevels: a list. Used to change the contrasts from the default treatment contrasts to treatment contrasts with a chosen omitted group (the reference group). To do this, the user puts an element on the list with the same name as a variable to change contrasts on and then make the value for that list element equal to the value that should be the omitted group (the reference group).
jrrIMax: a numeric value; when using the jackknife variance estimation method, the default estimation option, jrrIMax=1, uses the sampling variance from the first plausible value as the component for sampling variance estimation. The \(V_{jrr}\) term (see Statistical Methods Used in EdSurvey) can be estimated with any number of plausible values, and values larger than the number of plausible values on the survey (including Inf) will result in all plausible values being used. Higher values of jrrIMax lead to longer computing times and more accurate variance estimates.
dropOmittedLevels: a logical value. When set to the default value of TRUE, drops those levels of all factor variables that are specified in edsurvey.data.frame. Use print on an edsurvey.data.frame to see the omitted levels.
defaultConditions: a logical value. When set to the default value of TRUE, uses the default conditions stored in edsurvey.data.frame to subset the data. Use print on an edsurvey.data.frame to see the default conditions.
recode: a list of lists to recode variables. Defaults to NULL. Can be set as recode = list(var1= list(from=c("a","b","c"), to ="d")).
returnVarEstInputs: a logical value. Set to TRUE to return the inputs to the jackknife and imputation variance estimates, which allow for computation of covariances between estimates.
estMethod: a character value indicating which estimation method to use. Default is OLS; other option is GLS.
verbose: logical; indicates whether a detailed printout should display during execution
omittedLevels: this argument is deprecated. Use dropOmittedLevels

Value

An edsurvey.mvrlm with elements:

call: the function call
formula: the formula used to fit the model
coef: the estimates of the coefficients
se: the standard error estimates of the coefficients
Vimp: the estimated variance caused by uncertainty in the scores (plausible value variables)
Vjrr: the estimated variance caused by sampling
M: the number of plausible values
varm: the variance estimates under the various plausible values
coefm: the values of the coefficients under the various plausible values
coefmat: the coefficient matrix (typically produced by the summary of a model)
r.squared: the coefficient of determination
weight: the name of the weight variable
npv: the number of plausible values
njk: the number of the jackknife replicates used
varEstInputs: When returnVarEstInputs is TRUE, this element is returned. These are used for calculating covariances with varEstToCov.
residuals: residuals for each of the PV models
fitted.values: model fitted values
residCov: residual covariance matrix for dependent variables
residPV: residuals for each dependent variable
inputs: coefficient estimation input matrices
n0: full data n
nUsed: n used for model
B: imputation variance-covariance matrix, before multiplication by (M+1)/M
U: sampling variance-covariance matrix

Details

This function implements an estimator that correctly handles multiple left-hand side variables that are either numeric or plausible values, allows for survey sampling weights, and estimates variances using the jackknife replication method. The vignette titled Statistical Methods Used in EdSurvey describes estimation of the reported statistics.

The coefficients are estimated using the sample weights according to the section “Estimation of Weighted Means When Plausible Values Are Not Present” or the section “Estimation of Weighted Means When Plausible Values Are Present,” depending on if there are assessment variables or variables with plausible values in them.

The coefficient of determination (R-squared value) is similarly estimated by finding the average R-squared using the sample weights for each set of plausible values.

Variance estimation of coefficients

All variance estimation methods are shown in the vignette titled Statistical Methods Used in EdSurvey.

When the predicted value does not have plausible values, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Not Present, Using the Jackknife Method.”

When plausible values are present, the variance of the coefficients is estimated according to the section “Estimation of Standard Errors of Weighted Means When Plausible Values Are Present, Using the Jackknife Method.”

For more information on the specifics of multivariate regression, see the vignette titled Methods and Overview of Using EdSurvey for Multivariate Regression.

Author

Alex Lishinski and Paul Bailey

Examples

if (FALSE) { # \dontrun{
# read in the example data (generated, not real student data)
sdf <- readNAEP(path=system.file("extdata/data", "M36NT2PM.dat", package = "NAEPprimer"))

# use | symbol to separate dependent variables in the left-hand side of formula
mvrlm.fit <- mvrlm.sdf(formula=algebra | geometry ~ dsex + m072801, jrrIMax = 5, data = sdf)

# print method returns coefficients, as does coef method
mvrlm.fit
coef(mvrlm.fit)

# for more detailed results, use summary:
summary(mvrlm.fit)

# details of model can also be accessed through components of the returned object; for example:

# coefficients (one column per dependent variable)
mvrlm.fit$coef
# coefficient table with standard errors and p-values (1 table per dependent variable)
mvrlm.fit$coefmat
# R-squared values (one per dependent variable)
mvrlm.fit$r.squared
# residual covariance matrix
mvrlm.fit$residCov

# dependent variables can have plausible values or not (or a combination)

mvrlm.fit <- mvrlm.sdf(formula=composite | mrps22 ~ dsex + m072801, data = sdf, jrrIMax = 5)
summary(mvrlm.fit)

mvrlm.fit <- mvrlm.sdf(formula=algebra | geometry | measurement ~ dsex + m072801,
                     data = sdf, jrrIMax = 5)
summary(mvrlm.fit)

mvrlm.fit <- mvrlm.sdf(formula=mrps51 | mrps22 ~ dsex + m072801, data = sdf, jrrIMax = 5)
summary(mvrlm.fit)

# hypotheses about coefficient restrictions can also be tested using the Wald test

mvr <- mvrlm.sdf(formula=algebra | geometry ~ dsex + m072801, data = sdf)

hypothesis <- c("geometry_dsexFemale = 0", "algebra_dsexFemale = 0")

# test statistics based on the F and chi-squared distribution are available
linearHypothesis(model=mvr, hypothesis = hypothesis, test = "F")
linearHypothesis(model=mvr, hypothesis = hypothesis, test = "Chisq")
} # }