repTable {eatRep}

JK1, JK2 and BRR for frequency tables and trend estimation.

Description

Compute frequency tables for categorical variables (e.g. factors: dichotomous or polytomous) in complex cluster designs. Estimation of standard errors optionally takes the clustered structure and multiple imputed variables into account. To date, Jackknife-1 (JK1), Jackknife-2 (JK2) and Balanced repeated replicate (BRR) methods are implemented to account for clustered designs. Procedures of Rubin (1987) and Rubin (2003) are implemented to account for multiple imputed data and nested imputed data, if necessary. Conceptually, the function combines replication and imputation methods. Technically, this is a wrapper for the svymean function of the survey package.

Usage

repTable(datL, ID, wgt = NULL, type = c("none", "JK2", "JK1", "BRR", "Fay"), PSU = NULL,
          repInd = NULL, jkfac=NULL, repWgt = NULL, nest=NULL, imp=NULL, groups = NULL,
          group.splits = length(groups), group.differences.by = NULL,
          cross.differences = FALSE, crossDiffSE = c("wec", "rep","old"),
          nBoot = 100, chiSquare = FALSE, correct = TRUE, group.delimiter = "_",
          trend = NULL, linkErr = NULL, dependent, separate.missing.indicator = FALSE,
          na.rm=FALSE, expected.values = NULL, doCheck = TRUE, forceTable = FALSE,
          engine = c("survey", "BIFIEsurvey"), scale = 1, rscales = 1, mse=TRUE,
          rho=NULL, verbose = TRUE, progress = TRUE )

Arguments

datL

Data frame in the long format (i.e. each line represents one ID unit in one imputation of one nest) containing all variables for analysis.

ID

Variable name or column number of student identifier (ID) variable. ID variable must not contain any missing values.

wgt

Optional: Variable name or column number of weighting variable. If no weighting variable is specified, all cases will be equally weighted.

type

Defines the replication method for cluster replicates which is to be applied. Depending on type, additional arguments must be specified (e.g., PSU and/or repInd or repWgt).

PSU

Variable name or column number of variable indicating the primary sampling unit (PSU). When a jackknife procedure is applied, the PSU is the jackknife zone variable. If NULL, no cluster structure is assumed and standard errors are computed according to a random sample.

repInd

Variable name or column number of variable indicating replicate ID. In a jackknife procedure, this is the jackknife replicate variable. If NULL, no cluster structure is assumed and standard errors are computed according to a random sample.

jkfac

Only applies if engine = "BIFIEsurvey". Argument is passed to BIFIE.data.jack and specifies the factor for multiplying jackknife replicate weights.

repWgt

Normally, replicate weights are created by repTable directly from PSU and repInd variables. Alternatively, if replicate weights are included in the data.frame, specify the variable names or column number in the repWgt argument.

nest

Optional: name or column number of the nesting variable. Only applies in nested multiple imputed data sets.

imp

Optional: name or column number of the imputation variable. Only applies in multiple imputed data sets.

groups

Optional: vector of names or column numbers of one or more grouping variables.

group.splits

Optional: If groups are defined, group.splits optionally specifies whether analysis should be done also in the whole group or overlying groups. See examples for more details.

group.differences.by

Optional: Specifies one grouping variable for which a chi-square test should be applied. The corresponding variable must be included in the groups statement. If specified, the distribution of the dependent variable is compared between the groups. See examples for further details.

cross.differences

Either a list of vectors, specifying the pairs of levels for which cross-level differences should be computed. Alternatively, if TRUE, cross-level differences for all pairs of levels are computed. If FALSE, no cross-level differences are computed. (see examples 2a, 3, and 4 in the help file of the repMean function)

crossDiffSE

Method for standard error estimation for cross level differences, where groups are dependent. wec uses weighted effect coding, rep uses replication methods (bootstrap or jackknife) to estimate the standard error between the total mean and group-specific means. old does not account for dependent groups and treat the groups as if they were independent from each other.

nBoot

Without replicates (i.e., for completely random samples), the rep method for standard error estimation for cross level differences needs a bootstrap. nBoot therefore specifies the number of bootstrap samples. This argument is only necessary, if crossDiffSE = "rep" and none of the replicate methods (JK1, JK2, or BRR) is applied. Otherwise, nBoot will be ignored.

chiSquare

Logical. Applies only if group.differences.by was specified. Defines whether group differences should be represented in a chi square test or in (mean) differences of each group's relative frequency. Note: To date, chi square test is not available for engine = "BIFIEsurvey".

correct

Logical. Applies only if 'group.differences.by' is requested without cluster replicates. A logical indicating whether to apply continuity correction when computing the test statistic for 2 by 2 tables. See help page of 'chisq.test' for further details.

group.delimiter

Character string which separates the group names in the output frame.

trend

Optional: name or column number of the trend variable. Note: Trend variable must have exact two levels. Levels for grouping variables must be equal in both 'sub populations' partitioned by the trend variable.

linkErr

Optional: Either the name or column number of the linking error variable. If NULL, a linking error of 0 will be assumed in trend estimation. Alternatively, linking errors may be given as data.frame with following specifications: Two columns, named trendLevel1 and trendLevel2 which contain the levels of the trend variable. The contrasts between both values indicates which trend is meant. For only two measurement occasions, i.e. 2010 and 2015, trendLevel1 should be 2010, and trendLevel2 should be 2015. For three measurement occasions, i.e. 2010, 2015, and 2020, additional lines are necessary where trendLevel1 should be 2010, and trendLevel2 should be 2020, to mark the contrast between 2010 and 2020, and further additional lines are necessary where trendLevel1 should be 2015, and trendLevel2 should be 2020. The column depVar must include the name of the dependent variable. This string must correspond to the name of the dependent variable in the data. The column parameter indicates the parameter the linking error belongs to. Column linkingError includes the linking error value. Providing linking error in a data.frame is necessary for more than two measurement occasions. See the fourth example below for further details.

dependent

Variable name or column number of the dependent variable.

separate.missing.indicator

Logical. Should frequencies of missings in dependent variable be integrated? Note: That is only useful if missing occur as NA. If the dependent variable is coded as character, for example 'male', 'female', 'missing', separate missing indicator is not necessary.

na.rm

Logical: Should cases with missing values be dropped?

expected.values

Optional. A vector of values expected in dependent variable. Recommend to left this argument empty.

doCheck

Logical: Check the data for consistency before analysis? If TRUE groups with insufficient data are excluded from analysis to prevent subsequent functions from crashing.

forceTable

Logical: Function decides internally whether the table or the mean function of survey is called. If the mean function is called, the polytomous dependent variable is converted to dichotomous indicator variables. If mean is called, group differences for each category of the polytomous dependent variable can be computed. If table is called, a chi square statistic may be computed. The argument allows to force the function either to call mean or table.

engine

Which package should be used for estimation?

scale

scaling constant for variance, for details, see help page of svrepdesign from the survey package

rscales

scaling constant for variance, for details, see help page of svrepdesign from the survey package

mse

Logical: If TRUE, compute variances based on sum of squares around the point estimate, rather than the mean of the replicates. See help page of svrepdesign from the survey package for further details.

rho

Shrinkage factor for weights in Fay's method. If engine = "survey", argument is passed to the rho argument of the svrepdesign function from the survey package. See the corresponding help page for further details. If engine = "BIFIEsurvey", argument is passed to the fayfac argument of the BIFIE.data.jack function from the BIFIEsurvey package. See the corresponding help page for further details. For convenience, if rho = NULL (the default) and engine = "BIFIEsurvey" and type = "JK1", BIFIE.data.jack is called with jktype="JK_GROUP" and fayfac = rho, where \rho = (N_{cluster} - 1) \times N_{cluster}^{-1}

verbose

Logical: Show analysis information on console?

progress

Logical: Show progress bar on console?

Details

Function first creates replicate weights based on PSU and repInd variables according to JK2 procedure implemented in WesVar. According to multiple imputed data sets, a workbook with several analyses is created. The function afterwards serves as a wrapper for svymean called by svyby implemented in the survey package. Relative frequencies of the categories of the dependent variable are computed by the means of the dichotomous indicators (e.g. dummy variables) of each category. The results of the several analyses are then pooled according to Rubin's rule, which is adapted for nested imputations if the dependent argument implies a nested structure.

Value

A list of data frames in the long format. The output can be summarized using the report function. The first element of the list is a list with either one (no trend analyses) or two (trend analyses) data frames with at least six columns each. For each subpopulation denoted by the groups statement, each dependent variable, each parameter (i.e., the values of the corresponding categories of the dependent variable) and each coefficient (i.e., the estimate and the corresponding standard error) the corresponding value is given.

group

Denotes the group an analysis belongs to. If no groups were specified and/or analysis for the whole sample were requested, the value of ‘group’ is ‘wholeGroup’.

depVar

Denotes the name of the dependent variable in the analysis.

modus

Denotes the mode of the analysis. For example, if a JK2 analysis without sampling weights was conducted, ‘modus’ takes the value ‘jk2.unweighted’. If a analysis without any replicates but with sampling weights was conducted, ‘modus’ takes the value ‘weighted’.

parameter

Denotes the parameter of the regression model for which the corresponding value is given further. For frequency tables, this is the value of the category of the dependent variable which relative frequency is given further.

coefficient

Denotes the coefficient for which the corresponding value is given further. Takes the values ‘est’ (estimate) and ‘se’ (standard error of the estimate).

value

The value of the parameter, i.e. the relative frequency or its standard error.

If groups were specified, further columns which are denoted by the group names are added to the data frame.

References

Rubin, D.B. (2003): Nested multiple imputation of NMES via partially incompatible MCMC. Statistica Neerlandica 57, 1, 3–18.

Examples

data(lsa)

### Example 1: only means, SD and variances for each country
### subsetting: We only consider domain 'reading'
rd     <- lsa[which(lsa[,"domain"] == "reading"),]

### We only consider the first "nest".
rdN1   <- rd[which(rd[,"nest"] == 1),]

### First, we only consider year 2010
rdN1y10<- rdN1[which(rdN1[,"year"] == 2010),]

### First example: Computes frequencies of polytomous competence levels (1, 2, 3, 4, 5)
### conditionally on country, using a chi-square test to decide whether the distribution
### varies between countries (it's an overall test, i.e. with three groups, df1=8).
freq.tab1 <- repTable(datL = rdN1y10, ID = "idstud", wgt = "wgt", imp="imp",
             type = "JK2", PSU = "jkzone", repInd = "jkrep", groups = "country",
             group.differences.by = "country", dependent = "comp", chiSquare = TRUE)
res1      <- report(freq.tab1, add = list ( domain = "reading" ))


### Second example: Computes frequencies of polytomous competence levels (1, 2, 3, 4, 5)
### conditionally on country. Now we test whether the frequency of each single category
### differs between pairs of countries (it's not an overall test ... repTable now
### calls repMean internally, using dummy variables
freq.tab2 <- repTable(datL = rdN1y10, ID = "idstud", wgt = "wgt", imp="imp",
             type = "JK2", PSU = "jkzone", repInd = "jkrep", groups = "country",
             group.differences.by = "country", dependent = "comp", chiSquare = FALSE)
res2      <- report(freq.tab2, add = list ( domain = "reading" ))

### Third example: trend estimation and nested imputation and 'by' loop
### (to date, only crossDiffSE = "old" works)
freq.tab3 <- by ( data = lsa, INDICES = lsa[,"domain"], FUN = function (subdat) {
             repTable(datL = subdat, ID = "idstud", wgt = "wgt", imp="imp",
                 nest = "nest", type = "JK2", PSU = "jkzone", repInd = "jkrep",
                 groups = "country", group.differences.by = "country",
                 group.splits = 0:1, cross.differences = TRUE, crossDiffSE = "old",
                 dependent = "comp", chiSquare = FALSE, trend = "year",
                 linkErr = "leComp") })
res3      <- do.call("rbind", lapply(names(freq.tab3), FUN = function (domain) {
             report(freq.tab3[[domain]], trendDiffs = TRUE,
                    add = list ( domain = domain ))
             }))
             
### Fourth example: similar to example 3. trend estimation using a linking
### error data.frame
linkErrs  <- data.frame ( trendLevel1 = 2010, trendLevel2 = 2015,  depVar = "comp",
             unique(lsa[,c("domain", "comp", "leComp")]), stringsAsFactors = FALSE)
colnames(linkErrs) <- car::recode(colnames(linkErrs),
                      "'comp'='parameter'; 'leComp'='linkingError'")
freq.tab4 <- by ( data = lsa, INDICES = lsa[,"domain"], FUN = function (subdat) {
             repTable(datL = subdat, ID = "idstud", wgt = "wgt", type="none",
                 imp="imp", nest = "nest", groups = "country",
                 group.differences.by = "country", group.splits = 0:1,
                 cross.differences = FALSE, dependent = "comp", chiSquare = FALSE,
                 trend = "year",
                 linkErr = linkErrs[which(linkErrs[,"domain"] == subdat[1,"domain"]),])
             })
res4      <- do.call("rbind", lapply(names(freq.tab4), FUN = function (domain) {
             report(freq.tab4[[domain]], trendDiffs = TRUE,
                    add = list ( domain = domain ))
             }))

### Fifth example: minimal example for three measurement occasions
### borrow data from the eatGADS package
trenddat1 <- system.file("extdata", "trend_gads_2010.db", package = "eatGADS")
trenddat2 <- system.file("extdata", "trend_gads_2015.db", package = "eatGADS")
trenddat3 <- system.file("extdata", "trend_gads_2020.db", package = "eatGADS")
trenddat  <- eatGADS::getTrendGADS(filePaths = c(trenddat1, trenddat2, trenddat3),
             years = c(2010, 2015, 2020), fast=FALSE)
dat       <- eatGADS::extractData(trenddat)
### use template linking Error Object
load(system.file("extdata", "linking_error.rda", package = "eatRep"))
### check consistency of data and linking error object
check1 <- checkLEs(c(trenddat1, trenddat2, trenddat3), lErr)
### Analysis for reading comprehension
freq.tab5 <- repTable(datL = dat[which(dat[,"dimension"] == "reading"),],
             ID = "idstud", type="none", imp="imp", dependent = "traitLevel",
             chiSquare = FALSE, trend = "year",
             linkErr = lErr[which(lErr[,"domain"] == "reading"),])
res5      <- report(freq.tab5, trendDiffs = TRUE, add = list ( domain = "reading" ))