repse: Standard Error for Estimates with Replicate Weights and Plausible Values

Description

Calculates the standard error given a vector or list of previous estimations.

Usage

repse(
  er,
  e0,
  setup = NULL,
  method = c("TIMSS", "PIRLS", "ICILS", "ICCS", "PISA", "TALIS")
)
repsecomp(se)
pvse(PVse, PVe0, df = FALSE)

Value

the standard error.

Arguments

er: a vector or a list containing any statistic of interest (e.g., percent, mean, variance, regression coefficient). If it is a vector or list of length==1, the function estimates standard errors without plausible values. If it is a list with length>1, it estimates standard errors with plausible values.
e0: a numeric vector or a vector containing any statistic of interest (e.g., percent, mean, variance, regression coefficient), computed using total weights. For scenarios without plausible values, e0 should be a single value. For scenarios with plausible values, e0 should be a vector of the same length as er.
setup: an optional list produced by repsetup.
method: a string indicating the name of the large-scale assessment to determine the replication method to use. Available options are: "TIMSS", "PIRLS", "ICILS", "ICCS", "PISA", and "TALIS". Note that "TIMSS" and "PIRLS" refer to the method used from 2016 onwards. Their method has not yet been implemented for previous cycles.
se: a numeric vector with standard errors, used by repsecomp() to estimate a composite standard error.
PVse: a numeric vector containing the standard errors of the estimates of each plausible value.
PVe0: a numeric vector containing the point estimates of each plausible value.
df: a logical value indicating if degrees should be calculated.

Details

The standard errors are calculated using a modifier $m$, for TIMSS and ICILS: $m = 0.5$; for ICILS and ICCS: $m = 1$; and for PISA and TALIS: $\frac{1}{R(1-0.5)^2}$. Depending on the statistic, one of the following formulas is used.

The standard error not involving plausible values is calculated by:

$$\sqrt{m\times \sum_{r=1}^{R}(\varepsilon_r-\varepsilon_0)^2}.$$

The standard error involving plausibles values and replicate weights is calculated by:

$$\sqrt{\left[ \sum_{p=1}^{P} \left( m\times \sum_{r=1}^{R}(\varepsilon_{rp}-\varepsilon_{0p})^2 \right) \dfrac{1}{P}\right]+ \left[ \left(1+ \dfrac{1}{P} \right) \dfrac{\sum_{p=1}^{P} (\varepsilon_{0p}-\overline{\varepsilon}_{0p})^{2}}{P-1} \right]}.$$

The standard error involving plausibles values without replicate weights is calculated by:

$$\sqrt{ \dfrac{\sum_{p=1}^{P} SE^2_{\varepsilon_{0P}}}{P}+ \left[ \left(1+ \dfrac{1}{P} \right) \dfrac{\sum_{p=1}^{P} (\varepsilon_{0p}-\overline{\varepsilon}_{0p})^{2}}{P-1} \right]}.$$

The standard error of the difference of two statistics ($a$ and $b$) from independent samples is calculated by:

$$\sqrt{SE_a^{2}+SE_b^{2}}.$$

The standard error of the difference of two statistics ($a$ and $b$) from dependent samples not involving plausible values is calculated by:

$$\sqrt{m\times \sum_{r=1}^R((a_r-b_r)-(a_0-b_0))^2}.$$

The standard error of the difference of two statistics ($a$ and $b$) from dependent samples involving plausible values is calculated by:

$$\sqrt{\left[ \sum_{p=1}^{P} \left( m\times \sum_{r=1}^{R}((a_{rp}-b_{rp})-(a_{0p}-b_{0p}))^2 \right) \dfrac{1}{P}\right]+ \left[ \left(1+ \dfrac{1}{P} \right) \dfrac{\sum_{p=1}^{P} \left((a_{0p}-b_{0p})- ( \overline{a}_{0p}-\overline{b}_{0p}) \right)^{2}}{P-1} \right]}.$$

The standard error of a composite estimate is calculated by:

$$\sqrt{\dfrac{\sum_{c=1}^CSE^2_{\varepsilon_c}}{C^{2}}}.$$

The standard error of the difference between an element ($a$) of the composite and the composite is calculated by:

$$\sqrt{\dfrac{\sum_{c=1}^CSE^2_{\varepsilon_c}}{C^{2}}+\left(\dfrac{(C-1)^2-1}{C^2}\right)SE^2_a}.$$

Where $\varepsilon$ represents a statistic of interest, the subindex $0$ indicates an estimate using the total weights, $r$ indicates a replicate from a total of $R$, $p$ indicates a plausible value from a total of $P$, and $c$ indicates an element in a composite estimate from value a total of $C$.

Examples

Run this code

# Creation of replicate weights
RW <- repcreate(df = repdata, # the data frame with all the information
                wt = "wt", # the total weights column name
                jkzone = "jkzones", # the jkzones column name
                jkrep = "jkrep", # the jkreps column name
                repwtname = "REPWT", # the desired name for the rep weights
                reps = 50, # the number of replications
                method = "ICILS") # the name of the method aka the study name

# Non-PVs ----

## Mean with total weights
E0 <- stats::weighted.mean(x = repdata$item01, w = repdata$wt, na.rm = TRUE)
E0

## Means by replication
ER <- as.vector(apply(RW,2,function(i){
  stats::weighted.mean(x = repdata$item01, w = i, na.rm = TRUE)
}))
ER

## Standard error by hand
repse(er = ER, e0 = E0, method = "ICILS")

## Standard error with repmean()
repmean(x = "item01",wt = "wt",repwt = RW,df = repdata, method = "ICILS")


# PVs ----

## Mean with total weights
E0 <- sapply(1:5,function(i){
  stats::weighted.mean(x = repdata[,paste0("Math",i)], w = repdata$wt,
                       na.rm = TRUE)
})
E0

## Means by replication
ER <- lapply(1:5, function(j){
  as.vector(apply(RW,2,function(i){
    stats::weighted.mean(x = repdata[,paste0("Math",j)], w = i, na.rm = TRUE)
  }))
})
ER

## Standard error by hand
repse(er = ER, e0 = E0, method = "ICILS")

## Standard error with repmean()
repmean(x = paste0("Math",1:5),wt = "wt",repwt = RW,df = repdata, method = "ICILS",PV = TRUE)

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