R/imputationSummary.R
In CenterForAssessment/cfaTools: Center for Assessment Tools for Large Scale Educational Assessment Analysis
Defines functions
`imputationSummary`
`imputationSummary` <- function(
data.to.summarize,
institution.level = NULL,
summary.level = NULL,
standardize.scores = NULL
) {
### Utility functions
se <- function(x, na.rm=FALSE) {
if (na.rm) x <- na.omit(x)
sqrt(var(x)/length(x))
}
Z <- function(x, y = NULL, rm.na = TRUE) {
if (is.null(y)) y <- x
(x - mean(y, na.rm = rm.na)) / sd(y, na.rm = rm.na)
}
### Avoid "Undefined global functions or variables:" from R CMD check
SCALE_SCORE_OBSERVED <- SGP_BASELINE_OBSERVED <- SGP_OBSERVED <- SS_OBS_ORIG_SCALE <-
Mean_SS_Observed <- Mean_SGPB_Observed <- Mean_SGP_Observed <-
Mean_SS_Imputed <- Mean_SGP_Imputed <- Mean_SGPB_Imputed <- N <- IMP_N <- SGPB_ADF <-
SGPB_B <- SGPB_CI_high <- SGPB_CI_high_simp <- SGPB_CI_low <- SGPB_CI_low_simp <-
SGPB_F_Simp <- SGPB_F_Stat <- SGPB_F_p <- SGPB_F_p_simp <- SGPB_Gamma <-
SGPB_Lamda <- SGPB_RIV <- SGPB_T <- SGPB_U_Imp <- SGPB_U_bar <- SGPB_tSimp <-
SGPB_tStat <- SGP_ADF <- SGP_B <- SGP_CI_high <- SGP_CI_high_simp <- SGP_CI_low <-
SGP_CI_low_simp <- SGP_F_Simp <- SGP_F_Stat <- SGP_F_p <- SGP_F_p_simp <-
SGP_Gamma <- SGP_Lamda <- SGP_RIV <- SGP_T <- SGP_U_Imp <- SGP_U_bar <- SGP_tSimp <-
SGP_tStat <- SS_ADF <- SS_B <- SS_CI_high <- SS_CI_high_simp <- SS_CI_low <-
SS_CI_low_simp <- SS_F_Simp <- SS_F_Stat <- SS_F_p <- SS_F_p_simp <- SS_Gamma <-
SS_Lamda <- SS_RIV <- SS_T <- SS_U_Imp <- SS_U_bar <- SS_tSimp <- SS_tStat <- NULL
M.IMP <- length(grep("SCALE_SCORE_IMPUTED_", names(data.to.summarize)))
#####
### summarize at institution.level and summary.level first -- 1 for each imputation
### This is eq Qhat_l 2.16 -- https://stefvanbuuren.name/fimd/sec-whyandwhen.html
#####
if (!is.null(standardize.scores)) {
data.to.summarize[, SS_OBS_ORIG_SCALE := SCALE_SCORE_OBSERVED]
data.to.summarize[, SCALE_SCORE_OBSERVED := Z(SCALE_SCORE_OBSERVED), by = standardize.scores] # list(get(standardize.scores))
}
smry_obs <- data.to.summarize[, list(
Mean_SS_Observed = mean(SCALE_SCORE_OBSERVED, na.rm = TRUE),
SE_SS_Observed = se(SCALE_SCORE_OBSERVED, na.rm = TRUE),
Mean_SGP_Observed = mean(SGP_OBSERVED, na.rm = TRUE),
SE_SGP_Observed = se(SGP_OBSERVED, na.rm = TRUE),
Mean_SGPB_Observed = mean(SGP_BASELINE_OBSERVED, na.rm = TRUE),
SE_SGPB_Observed = se(SGP_BASELINE_OBSERVED, na.rm = TRUE),
Percent_Missing = (sum(is.na(SCALE_SCORE_OBSERVED))/.N)*100, N=.N),
keyby = c(institution.level, summary.level)]
smry_imp <- data.table()
for (IMP in seq(M.IMP)) {
ss.imp <- paste0("SCALE_SCORE_IMPUTED_", IMP)
sgp.imp <- paste0("SGP_IMPUTED_", IMP)
sgpb.imp <- paste0("SGP_BASELINE_IMPUTED_", IMP)
if (!is.null(standardize.scores)) {
data.to.summarize[, eval(ss.imp) := Z(x = get(ss.imp), y = SS_OBS_ORIG_SCALE), by = standardize.scores]
}
tmp_imp_smry <- data.to.summarize[, list(
Mean_SS_Imputed = mean(get(ss.imp), na.rm = TRUE), # Q_l_SS
SS_U_Imp = var(get(ss.imp), na.rm = TRUE), # Ubar_l_SS
Mean_SGP_Imputed = mean(get(sgp.imp), na.rm = TRUE), # Q_l_SGP
SGP_U_Imp = var(get(sgp.imp), na.rm = TRUE), # Ubar_l_SGP
Mean_SGPB_Imputed = mean(get(sgpb.imp), na.rm = TRUE), # Q_l_SGP_Baseline
SGPB_U_Imp = var(get(sgpb.imp), na.rm = TRUE)), # Ubar_l_SGP_Baseline
keyby = c(institution.level, summary.level)][, IMP_N := IMP]
smry_imp <- rbindlist(list(smry_imp, tmp_imp_smry))
}
#####
### Pool results at institution.level and summary.level over imputations
#####
M.IMP <- max(smry_imp$IMP_N)
smry_imp_pool <- smry_imp[, list(
Mean_SS_Imputed = mean(Mean_SS_Imputed, na.rm = TRUE),
SS_U_bar = mean(SS_U_Imp, na.rm = TRUE),
SS_B = var(Mean_SS_Imputed),
Mean_SGP_Imputed = mean(Mean_SGP_Imputed, na.rm = TRUE),
SGP_U_bar = mean(SGP_U_Imp, na.rm = TRUE),
SGP_B = var(Mean_SGP_Imputed),
Mean_SGPB_Imputed = mean(Mean_SGPB_Imputed, na.rm = TRUE),
SGPB_U_bar = mean(SGPB_U_Imp, na.rm = TRUE),
SGPB_B = var(Mean_SGPB_Imputed)),
keyby=c(institution.level, summary.level)]
smry_all <- smry_obs[smry_imp_pool]
base.names <- names(smry_all)
## T - Total Variance
smry_all[, SS_T := SS_U_bar + (1 + 1/M.IMP)*SS_B]
smry_all[, SGP_T := SGP_U_bar + (1 + 1/M.IMP)*SGP_B]
smry_all[, SGPB_T := SGPB_U_bar + (1 + 1/M.IMP)*SGPB_B]
### Variance Ratios :: 2.3.5
## Lambda -- proportion of variation attributed to the missing data. eq 2.24
smry_all[, SS_Lamda := round(((SS_B + SS_B/M.IMP)/SS_T), 5)]
smry_all[, SGP_Lamda := round(((SGP_B + SGP_B/M.IMP)/SGP_T), 5)]
smry_all[, SGPB_Lamda := round(((SGPB_B + SGPB_B/M.IMP)/SGPB_T), 5)]
## RIV (r) -- relative increase in variance due to nonresponse. eq 2.25
smry_all[, SS_RIV := round((SS_Lamda/(1-SS_Lamda)), 5)]
smry_all[, SGP_RIV := round((SGP_Lamda/(1-SGP_Lamda)), 5)]
smry_all[, SGPB_RIV := round((SGPB_Lamda/(1-SGPB_Lamda)), 5)]
## Adjusted Degrees of Freedom -- eq 2.31
smry_all[, SS_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SS_Lamda))]
smry_all[, SGP_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SGP_Lamda))]
smry_all[, SGPB_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SGPB_Lamda))]
## Gamma -- fraction of information about Q missing due to nonresponse
smry_all[, SS_Gamma := round((SS_RIV+(2/(SS_ADF+3)))/(1+SS_RIV), 5)]
smry_all[, SGP_Gamma := round((SGP_RIV+(2/(SGP_ADF+3)))/(1+SGP_RIV), 5)]
smry_all[, SGPB_Gamma := round((SGP_RIV+(2/(SGPB_ADF+3)))/(1+SGPB_RIV), 5)]
### Statistical Inference -- Section 2.4.2
## Confidence intervals
smry_all[!is.na(SS_ADF) & SS_ADF != 0, SS_tStat := qt(0.975, df=SS_ADF)*(sqrt(SS_T))]
smry_all[!is.na(SGP_ADF) & SGP_ADF != 0, SGP_tStat := qt(0.975, df=SGP_ADF)*(sqrt(SGP_T))]
smry_all[!is.na(SGPB_ADF) & SGPB_ADF != 0, SGPB_tStat := qt(0.975, df=SGPB_ADF)*(sqrt(SGPB_T))]
smry_all[!is.na(SS_tStat), SS_CI_low := Mean_SS_Imputed-SS_tStat]
smry_all[!is.na(SS_tStat), SS_CI_high := Mean_SS_Imputed+SS_tStat]
smry_all[!is.na(SGP_tStat), SGP_CI_low := Mean_SGP_Imputed - SGP_tStat]
smry_all[!is.na(SGP_tStat), SGP_CI_high := Mean_SGP_Imputed + SGP_tStat]
smry_all[!is.na(SGPB_tStat), SGPB_CI_low := Mean_SGPB_Imputed - SGPB_tStat]
smry_all[!is.na(SGPB_tStat), SGPB_CI_high := Mean_SGPB_Imputed + SGPB_tStat]
### Simplified Confidence Invervals - when you have entire population, see Vink and Van Buuren, 2014
nu <- M.IMP-1
qtSimp <- qt(0.975, df=nu)
## (1 + 1/M.IMP)*SS_B is the "simplified" T value (U_bar = 0)
smry_all[!is.na(SS_B) & SS_B != 0, SS_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SS_B))]
smry_all[!is.na(SGP_B) & SGP_B != 0, SGP_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SGP_B))]
smry_all[!is.na(SGPB_B) & SGPB_B != 0, SGPB_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SGPB_B))]
smry_all[!is.na(SS_tSimp), SS_CI_low_simp := Mean_SS_Imputed-SS_tSimp]
smry_all[!is.na(SS_tSimp), SS_CI_high_simp := Mean_SS_Imputed+SS_tSimp]
smry_all[!is.na(SGP_tSimp), SGP_CI_low_simp := Mean_SGP_Imputed - SGP_tSimp]
smry_all[!is.na(SGP_tSimp), SGP_CI_high_simp := Mean_SGP_Imputed + SGP_tSimp]
smry_all[!is.na(SGPB_tSimp), SGPB_CI_low_simp := Mean_SGPB_Imputed - SGPB_tSimp]
smry_all[!is.na(SGPB_tSimp), SGPB_CI_high_simp := Mean_SGPB_Imputed + SGPB_tSimp]
## F-test of NULL hypotheses (Observed vs Imputed)
smry_all[, SS_F_Stat := ((Mean_SS_Observed - Mean_SS_Imputed)^2)/SS_T]
smry_all[!is.na(SS_ADF) & SS_ADF != 0, SS_F_p := round(pf(SS_F_Stat, df1=1, df2=SS_ADF, lower.tail=FALSE), 5)]
smry_all[, SS_F_Simp := ((Mean_SS_Observed - Mean_SS_Imputed)^2)/((1 + 1/M.IMP)*SS_B)]
smry_all[, SS_F_p_simp := round(pf(SS_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
smry_all[, SGP_F_Stat := ((Mean_SGP_Observed - Mean_SGP_Imputed)^2)/SGP_T]
smry_all[!is.na(SGP_ADF) & SGP_ADF != 0, SGP_F_p := round(pf(SGP_F_Stat, df1=1, df2=SGP_ADF, lower.tail=FALSE), 5)]
smry_all[, SGP_F_Simp := ((Mean_SGP_Observed - Mean_SGP_Imputed)^2)/((1 + 1/M.IMP)*SGP_B)]
smry_all[, SGP_F_p_simp := round(pf(SGP_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
smry_all[, SGPB_F_Stat := ((Mean_SGPB_Observed - Mean_SGPB_Imputed)^2)/SGPB_T]
smry_all[!is.na(SGPB_ADF) & SGPB_ADF != 0, SGPB_F_p := round(pf(SGPB_F_Stat, df1=1, df2=SGPB_ADF, lower.tail=FALSE), 5)]
smry_all[, SGPB_F_Simp := ((Mean_SGPB_Observed - Mean_SGPB_Imputed)^2)/((1 + 1/M.IMP)*SGPB_B)]
smry_all[, SGPB_F_p_simp := round(pf(SGP_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
#####
### Overall Summary/Comparison of Imputed vs Observed
#####
overall_smry <- smry_all[, list(
Mean_SS_Diff = round(mean(Mean_SS_Observed-Mean_SS_Imputed, na.rm=TRUE), 3),
Cor_SS = round(cor(Mean_SS_Observed, Mean_SS_Imputed, use="na.or.complete"), 3),
Mean_SGP_Diff = round(mean(Mean_SGP_Observed-Mean_SGP_Imputed, na.rm=TRUE), 3),
Cor_SGP = round(cor(Mean_SGP_Observed, Mean_SGP_Imputed, use="na.or.complete"), 3),
Mean_SGPB_Diff = round(mean(Mean_SGPB_Observed-Mean_SGPB_Imputed, na.rm=TRUE), 3),
Cor_SGPB = round(cor(Mean_SGPB_Observed, Mean_SGPB_Imputed, use="na.or.complete"), 3)
), keyby=summary.level]
cols.to.keep <- c(institution.level, summary.level, "Percent_Missing", "N", grep("Mean_|SE_|Lambda|Gamma|RIV|_CI_|_F_p", names(smry_all), value=TRUE))
list(Summary = smry_all[, cols.to.keep, with=FALSE], Comparison = overall_smry)
}
CenterForAssessment/cfaTools documentation built on June 2, 2022, 9:23 a.m.
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Defines functions `imputationSummary`
`imputationSummary` <- function(
data.to.summarize,
institution.level = NULL,
summary.level = NULL,
standardize.scores = NULL
) {
### Utility functions
se <- function(x, na.rm=FALSE) {
if (na.rm) x <- na.omit(x)
sqrt(var(x)/length(x))
}
Z <- function(x, y = NULL, rm.na = TRUE) {
if (is.null(y)) y <- x
(x - mean(y, na.rm = rm.na)) / sd(y, na.rm = rm.na)
}
### Avoid "Undefined global functions or variables:" from R CMD check
SCALE_SCORE_OBSERVED <- SGP_BASELINE_OBSERVED <- SGP_OBSERVED <- SS_OBS_ORIG_SCALE <-
Mean_SS_Observed <- Mean_SGPB_Observed <- Mean_SGP_Observed <-
Mean_SS_Imputed <- Mean_SGP_Imputed <- Mean_SGPB_Imputed <- N <- IMP_N <- SGPB_ADF <-
SGPB_B <- SGPB_CI_high <- SGPB_CI_high_simp <- SGPB_CI_low <- SGPB_CI_low_simp <-
SGPB_F_Simp <- SGPB_F_Stat <- SGPB_F_p <- SGPB_F_p_simp <- SGPB_Gamma <-
SGPB_Lamda <- SGPB_RIV <- SGPB_T <- SGPB_U_Imp <- SGPB_U_bar <- SGPB_tSimp <-
SGPB_tStat <- SGP_ADF <- SGP_B <- SGP_CI_high <- SGP_CI_high_simp <- SGP_CI_low <-
SGP_CI_low_simp <- SGP_F_Simp <- SGP_F_Stat <- SGP_F_p <- SGP_F_p_simp <-
SGP_Gamma <- SGP_Lamda <- SGP_RIV <- SGP_T <- SGP_U_Imp <- SGP_U_bar <- SGP_tSimp <-
SGP_tStat <- SS_ADF <- SS_B <- SS_CI_high <- SS_CI_high_simp <- SS_CI_low <-
SS_CI_low_simp <- SS_F_Simp <- SS_F_Stat <- SS_F_p <- SS_F_p_simp <- SS_Gamma <-
SS_Lamda <- SS_RIV <- SS_T <- SS_U_Imp <- SS_U_bar <- SS_tSimp <- SS_tStat <- NULL
M.IMP <- length(grep("SCALE_SCORE_IMPUTED_", names(data.to.summarize)))
#####
### summarize at institution.level and summary.level first -- 1 for each imputation
### This is eq Qhat_l 2.16 -- https://stefvanbuuren.name/fimd/sec-whyandwhen.html
#####
if (!is.null(standardize.scores)) {
data.to.summarize[, SS_OBS_ORIG_SCALE := SCALE_SCORE_OBSERVED]
data.to.summarize[, SCALE_SCORE_OBSERVED := Z(SCALE_SCORE_OBSERVED), by = standardize.scores] # list(get(standardize.scores))
}
smry_obs <- data.to.summarize[, list(
Mean_SS_Observed = mean(SCALE_SCORE_OBSERVED, na.rm = TRUE),
SE_SS_Observed = se(SCALE_SCORE_OBSERVED, na.rm = TRUE),
Mean_SGP_Observed = mean(SGP_OBSERVED, na.rm = TRUE),
SE_SGP_Observed = se(SGP_OBSERVED, na.rm = TRUE),
Mean_SGPB_Observed = mean(SGP_BASELINE_OBSERVED, na.rm = TRUE),
SE_SGPB_Observed = se(SGP_BASELINE_OBSERVED, na.rm = TRUE),
Percent_Missing = (sum(is.na(SCALE_SCORE_OBSERVED))/.N)*100, N=.N),
keyby = c(institution.level, summary.level)]
smry_imp <- data.table()
for (IMP in seq(M.IMP)) {
ss.imp <- paste0("SCALE_SCORE_IMPUTED_", IMP)
sgp.imp <- paste0("SGP_IMPUTED_", IMP)
sgpb.imp <- paste0("SGP_BASELINE_IMPUTED_", IMP)
if (!is.null(standardize.scores)) {
data.to.summarize[, eval(ss.imp) := Z(x = get(ss.imp), y = SS_OBS_ORIG_SCALE), by = standardize.scores]
}
tmp_imp_smry <- data.to.summarize[, list(
Mean_SS_Imputed = mean(get(ss.imp), na.rm = TRUE), # Q_l_SS
SS_U_Imp = var(get(ss.imp), na.rm = TRUE), # Ubar_l_SS
Mean_SGP_Imputed = mean(get(sgp.imp), na.rm = TRUE), # Q_l_SGP
SGP_U_Imp = var(get(sgp.imp), na.rm = TRUE), # Ubar_l_SGP
Mean_SGPB_Imputed = mean(get(sgpb.imp), na.rm = TRUE), # Q_l_SGP_Baseline
SGPB_U_Imp = var(get(sgpb.imp), na.rm = TRUE)), # Ubar_l_SGP_Baseline
keyby = c(institution.level, summary.level)][, IMP_N := IMP]
smry_imp <- rbindlist(list(smry_imp, tmp_imp_smry))
}
#####
### Pool results at institution.level and summary.level over imputations
#####
M.IMP <- max(smry_imp$IMP_N)
smry_imp_pool <- smry_imp[, list(
Mean_SS_Imputed = mean(Mean_SS_Imputed, na.rm = TRUE),
SS_U_bar = mean(SS_U_Imp, na.rm = TRUE),
SS_B = var(Mean_SS_Imputed),
Mean_SGP_Imputed = mean(Mean_SGP_Imputed, na.rm = TRUE),
SGP_U_bar = mean(SGP_U_Imp, na.rm = TRUE),
SGP_B = var(Mean_SGP_Imputed),
Mean_SGPB_Imputed = mean(Mean_SGPB_Imputed, na.rm = TRUE),
SGPB_U_bar = mean(SGPB_U_Imp, na.rm = TRUE),
SGPB_B = var(Mean_SGPB_Imputed)),
keyby=c(institution.level, summary.level)]
smry_all <- smry_obs[smry_imp_pool]
base.names <- names(smry_all)
## T - Total Variance
smry_all[, SS_T := SS_U_bar + (1 + 1/M.IMP)*SS_B]
smry_all[, SGP_T := SGP_U_bar + (1 + 1/M.IMP)*SGP_B]
smry_all[, SGPB_T := SGPB_U_bar + (1 + 1/M.IMP)*SGPB_B]
### Variance Ratios :: 2.3.5
## Lambda -- proportion of variation attributed to the missing data. eq 2.24
smry_all[, SS_Lamda := round(((SS_B + SS_B/M.IMP)/SS_T), 5)]
smry_all[, SGP_Lamda := round(((SGP_B + SGP_B/M.IMP)/SGP_T), 5)]
smry_all[, SGPB_Lamda := round(((SGPB_B + SGPB_B/M.IMP)/SGPB_T), 5)]
## RIV (r) -- relative increase in variance due to nonresponse. eq 2.25
smry_all[, SS_RIV := round((SS_Lamda/(1-SS_Lamda)), 5)]
smry_all[, SGP_RIV := round((SGP_Lamda/(1-SGP_Lamda)), 5)]
smry_all[, SGPB_RIV := round((SGPB_Lamda/(1-SGPB_Lamda)), 5)]
## Adjusted Degrees of Freedom -- eq 2.31
smry_all[, SS_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SS_Lamda))]
smry_all[, SGP_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SGP_Lamda))]
smry_all[, SGPB_ADF := (((N-1)+1)/((N-1)+3))*((N-1)*(1-SGPB_Lamda))]
## Gamma -- fraction of information about Q missing due to nonresponse
smry_all[, SS_Gamma := round((SS_RIV+(2/(SS_ADF+3)))/(1+SS_RIV), 5)]
smry_all[, SGP_Gamma := round((SGP_RIV+(2/(SGP_ADF+3)))/(1+SGP_RIV), 5)]
smry_all[, SGPB_Gamma := round((SGP_RIV+(2/(SGPB_ADF+3)))/(1+SGPB_RIV), 5)]
### Statistical Inference -- Section 2.4.2
## Confidence intervals
smry_all[!is.na(SS_ADF) & SS_ADF != 0, SS_tStat := qt(0.975, df=SS_ADF)*(sqrt(SS_T))]
smry_all[!is.na(SGP_ADF) & SGP_ADF != 0, SGP_tStat := qt(0.975, df=SGP_ADF)*(sqrt(SGP_T))]
smry_all[!is.na(SGPB_ADF) & SGPB_ADF != 0, SGPB_tStat := qt(0.975, df=SGPB_ADF)*(sqrt(SGPB_T))]
smry_all[!is.na(SS_tStat), SS_CI_low := Mean_SS_Imputed-SS_tStat]
smry_all[!is.na(SS_tStat), SS_CI_high := Mean_SS_Imputed+SS_tStat]
smry_all[!is.na(SGP_tStat), SGP_CI_low := Mean_SGP_Imputed - SGP_tStat]
smry_all[!is.na(SGP_tStat), SGP_CI_high := Mean_SGP_Imputed + SGP_tStat]
smry_all[!is.na(SGPB_tStat), SGPB_CI_low := Mean_SGPB_Imputed - SGPB_tStat]
smry_all[!is.na(SGPB_tStat), SGPB_CI_high := Mean_SGPB_Imputed + SGPB_tStat]
### Simplified Confidence Invervals - when you have entire population, see Vink and Van Buuren, 2014
nu <- M.IMP-1
qtSimp <- qt(0.975, df=nu)
## (1 + 1/M.IMP)*SS_B is the "simplified" T value (U_bar = 0)
smry_all[!is.na(SS_B) & SS_B != 0, SS_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SS_B))]
smry_all[!is.na(SGP_B) & SGP_B != 0, SGP_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SGP_B))]
smry_all[!is.na(SGPB_B) & SGPB_B != 0, SGPB_tSimp := qtSimp*(sqrt((1 + 1/M.IMP)*SGPB_B))]
smry_all[!is.na(SS_tSimp), SS_CI_low_simp := Mean_SS_Imputed-SS_tSimp]
smry_all[!is.na(SS_tSimp), SS_CI_high_simp := Mean_SS_Imputed+SS_tSimp]
smry_all[!is.na(SGP_tSimp), SGP_CI_low_simp := Mean_SGP_Imputed - SGP_tSimp]
smry_all[!is.na(SGP_tSimp), SGP_CI_high_simp := Mean_SGP_Imputed + SGP_tSimp]
smry_all[!is.na(SGPB_tSimp), SGPB_CI_low_simp := Mean_SGPB_Imputed - SGPB_tSimp]
smry_all[!is.na(SGPB_tSimp), SGPB_CI_high_simp := Mean_SGPB_Imputed + SGPB_tSimp]
## F-test of NULL hypotheses (Observed vs Imputed)
smry_all[, SS_F_Stat := ((Mean_SS_Observed - Mean_SS_Imputed)^2)/SS_T]
smry_all[!is.na(SS_ADF) & SS_ADF != 0, SS_F_p := round(pf(SS_F_Stat, df1=1, df2=SS_ADF, lower.tail=FALSE), 5)]
smry_all[, SS_F_Simp := ((Mean_SS_Observed - Mean_SS_Imputed)^2)/((1 + 1/M.IMP)*SS_B)]
smry_all[, SS_F_p_simp := round(pf(SS_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
smry_all[, SGP_F_Stat := ((Mean_SGP_Observed - Mean_SGP_Imputed)^2)/SGP_T]
smry_all[!is.na(SGP_ADF) & SGP_ADF != 0, SGP_F_p := round(pf(SGP_F_Stat, df1=1, df2=SGP_ADF, lower.tail=FALSE), 5)]
smry_all[, SGP_F_Simp := ((Mean_SGP_Observed - Mean_SGP_Imputed)^2)/((1 + 1/M.IMP)*SGP_B)]
smry_all[, SGP_F_p_simp := round(pf(SGP_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
smry_all[, SGPB_F_Stat := ((Mean_SGPB_Observed - Mean_SGPB_Imputed)^2)/SGPB_T]
smry_all[!is.na(SGPB_ADF) & SGPB_ADF != 0, SGPB_F_p := round(pf(SGPB_F_Stat, df1=1, df2=SGPB_ADF, lower.tail=FALSE), 5)]
smry_all[, SGPB_F_Simp := ((Mean_SGPB_Observed - Mean_SGPB_Imputed)^2)/((1 + 1/M.IMP)*SGPB_B)]
smry_all[, SGPB_F_p_simp := round(pf(SGP_F_Simp, df1=1, df2=nu, lower.tail=FALSE), 5)]
#####
### Overall Summary/Comparison of Imputed vs Observed
#####
overall_smry <- smry_all[, list(
Mean_SS_Diff = round(mean(Mean_SS_Observed-Mean_SS_Imputed, na.rm=TRUE), 3),
Cor_SS = round(cor(Mean_SS_Observed, Mean_SS_Imputed, use="na.or.complete"), 3),
Mean_SGP_Diff = round(mean(Mean_SGP_Observed-Mean_SGP_Imputed, na.rm=TRUE), 3),
Cor_SGP = round(cor(Mean_SGP_Observed, Mean_SGP_Imputed, use="na.or.complete"), 3),
Mean_SGPB_Diff = round(mean(Mean_SGPB_Observed-Mean_SGPB_Imputed, na.rm=TRUE), 3),
Cor_SGPB = round(cor(Mean_SGPB_Observed, Mean_SGPB_Imputed, use="na.or.complete"), 3)
), keyby=summary.level]
cols.to.keep <- c(institution.level, summary.level, "Percent_Missing", "N", grep("Mean_|SE_|Lambda|Gamma|RIV|_CI_|_F_p", names(smry_all), value=TRUE))
list(Summary = smry_all[, cols.to.keep, with=FALSE], Comparison = overall_smry)
}
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