Just One G - II
Setup
#Packages
library(pacman)
p_load(dplyr, DT, meta, DescTools, ggplot2)
#Data
JOG <- read.csv("E:/Research/JustOneg/JOGMetaPART.csv")
datatable(JOG, extensions = c("Buttons", "FixedColumns"), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'print'), scrollX = T, fixedColumns = list(leftColumns = 3)))#Ad hoc functions
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
library(grid)
plots <- c(list(...), plotlist)
numPlots = length(plots)
if (is.null(layout)) {
layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
ncol = cols, nrow = ceiling(numPlots/cols))}
if (numPlots==1) {
print(plots[[1]])
} else {
grid.newpage()
pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
for (i in 1:numPlots) {
matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
layout.pos.col = matchidx$col))}}}Background
This is a meta-analysis of joint confirmatory factor analytic assessments of the indifference of the indicator. It will be expanded later to include a handful of new data points and results from other methods. These analyses have already been conducted and their results are in line with that presented below.
Analysis
JCFAs
Located at https://rpubs.com/JLLJ/JOG, https://rpubs.com/JLLJ/NJDH and https://rpubs.com/JLLJ/FRE20.
Meta-analytic Results
#Raw correlations
RCOR <- metacor(Corr,
sqrt(n),
data = JOG,
studlab = Source,
sm = "COR",
method.tau = "SJ")
#r-to-z transformed for proper variance estimation
ZCOR <- metacor(Corr,
sqrt(n),
data = JOG,
studlab = Source,
sm = "ZCOR",
method.tau = "SJ")
RCOR; ZCOR## COR 95%-CI %W(fixed) %W(random)
## Stone 92 0.9990 [ 0.9977; 1.0003] 3.6 2.5
## ByrdBuckhalt91 0.9990 [ 0.9974; 1.0006] 2.1 2.5
## TirreField2002A 0.9990 [ 0.9981; 0.9999] 6.3 2.5
## TirreField2002B 0.8900 [ 0.7942; 0.9858] 0.0 1.6
## TirreField2002C 0.9810 [ 0.9599; 1.0021] 0.0 2.4
## WothkeEA91 0.9990 [ 0.9980; 1.0000] 5.2 2.5
## Williamson69 0.9990 [ 0.9979; 1.0001] 4.8 2.5
## Kettner76A 0.9490 [ 0.9003; 0.9977] 0.0 2.2
## Kettner76B 0.9990 [ 0.9980; 1.0000] 5.9 2.5
## Palmer90 0.9750 [ 0.9526; 0.9974] 0.0 2.4
## KranzlerJensen91 0.3680 [-0.1953; 0.9313] 0.0 0.1
## LuoThompsonDetterman03 0.8700 [ 0.7686; 0.9714] 0.0 1.5
## Carey92 0.8900 [ 0.8188; 0.9612] 0.0 1.9
## AbrahamsEA94 0.8610 [ 0.8087; 0.9133] 0.0 2.2
## WolfeEA95 0.8660 [ 0.8179; 0.9141] 0.0 2.2
## NaglieriJensen87 0.9990 [ 0.9979; 1.0001] 4.5 2.5
## Engelhardt18 0.9800 [ 0.9651; 0.9949] 0.0 2.5
## StaufferReeCarretta96 0.9940 [ 0.9882; 0.9998] 0.2 2.5
## KeithKranzlerFlanagan01 0.9800 [ 0.9571; 1.0029] 0.0 2.4
## JohnsonEA04A 0.9900 [ 0.9813; 0.9987] 0.1 2.5
## JohnsonEA04B 0.9900 [ 0.9813; 0.9987] 0.1 2.5
## JohnsonEA04C 0.9990 [ 0.9981; 0.9999] 7.3 2.5
## JohnsonNijenhuisBouchard08A 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## JohnsonNijenhuisBouchard08A 0.8900 [ 0.8018; 0.9782] 0.0 1.7
## JohnsonNijenhuisBouchard08B 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## JohnsonNijenhuisBouchard08C 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## JohnsonNijenhuisBouchard08D 0.8100 [ 0.6642; 0.9558] 0.0 1.1
## JohnsonNijenhuisBouchard08E 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## JohnsonNijenhuisBouchard08F 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## JohnsonNijenhuisBouchard08G 0.7300 [ 0.5319; 0.9281] 0.0 0.7
## JohnsonNijenhuisBouchard08H 0.9300 [ 0.8727; 0.9873] 0.0 2.1
## JohnsonNijenhuisBouchard08I 0.9990 [ 0.9982; 0.9998] 7.9 2.5
## FloydEA10 0.9990 [ 0.9977; 1.0003] 3.3 2.5
## KaufmanEA12A 0.8600 [ 0.7872; 0.9328] 0.0 1.9
## KaufmanEA12B 0.8000 [ 0.7154; 0.8846] 0.0 1.7
## FloydEA12A 0.9700 [ 0.9380; 1.0020] 0.0 2.4
## FloydEA12B 0.9500 [ 0.8930; 1.0070] 0.0 2.1
## FloydEA12C 0.9990 [ 0.9978; 1.0002] 3.9 2.5
## FloydEA12D 0.8900 [ 0.7596; 1.0204] 0.0 1.2
## FloydEA12E 0.9200 [ 0.8143; 1.0257] 0.0 1.5
## Salthouse13 0.9100 [ 0.7943; 1.0257] 0.0 1.4
## ValeriusSparfeldt14A 0.9200 [ 0.8568; 0.9832] 0.0 2.0
## ValeriusSparfeldt14B 0.9900 [ 0.9818; 0.9982] 0.1 2.5
## ValeriusSparfeldt14C 0.9500 [ 0.9099; 0.9901] 0.0 2.3
## QuirogaEA15 0.9300 [ 0.8532; 1.0068] 0.0 1.8
## SwagermanEA16 0.9990 [ 0.9980; 1.0000] 5.4 2.5
## Lim88 0.9000 [ 0.8176; 0.9824] 0.0 1.8
##
## Number of studies combined: k = 47
##
## COR 95%-CI z p-value
## Fixed effect model 0.9989 [0.9987; 0.9992] 8238.10 0
## Random effects model 0.9581 [0.9380; 0.9782] 93.35 0
##
## Quantifying heterogeneity:
## tau^2 = 0.0042 [0.0013; 0.0051]; tau = 0.0647 [0.0362; 0.0717];
## I^2 = 78.1% [71.3%; 83.3%]; H = 2.14 [1.87; 2.45]
##
## Test of heterogeneity:
## Q d.f. p-value
## 210.38 46 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Untransformed correlations## COR 95%-CI %W(fixed) %W(random)
## Stone 92 0.9990 [ 0.9959; 0.9998] 0.8 2.0
## ByrdBuckhalt91 0.9990 [ 0.9925; 0.9999] 0.4 1.8
## TirreField2002A 0.9990 [ 0.9973; 0.9996] 1.6 2.1
## TirreField2002B 0.8900 [ 0.7322; 0.9571] 1.7 2.1
## TirreField2002C 0.9810 [ 0.9367; 0.9944] 1.1 2.1
## WothkeEA91 0.9990 [ 0.9969; 0.9997] 1.3 2.1
## Williamson69 0.9990 [ 0.9968; 0.9997] 1.2 2.1
## Kettner76A 0.9490 [ 0.8613; 0.9818] 1.5 2.1
## Kettner76B 0.9990 [ 0.9972; 0.9996] 1.5 2.1
## Palmer90 0.9750 [ 0.9360; 0.9904] 1.7 2.2
## KranzlerJensen91 0.3680 [-0.3382; 0.8091] 0.7 2.0
## LuoThompsonDetterman03 0.8700 [ 0.7141; 0.9437] 2.1 2.2
## Carey92 0.8900 [ 0.7889; 0.9442] 3.2 2.2
## AbrahamsEA94 0.8610 [ 0.7979; 0.9054] 9.7 2.2
## WolfeEA95 0.8660 [ 0.8084; 0.9072] 10.7 2.2
## NaglieriJensen87 0.9990 [ 0.9966; 0.9997] 1.1 2.1
## Engelhardt18 0.9800 [ 0.9569; 0.9908] 2.7 2.2
## StaufferReeCarretta96 0.9940 [ 0.9832; 0.9979] 1.5 2.1
## KeithKranzlerFlanagan01 0.9800 [ 0.9302; 0.9944] 1.0 2.1
## JohnsonEA04A 0.9900 [ 0.9749; 0.9960] 1.9 2.2
## JohnsonEA04B 0.9900 [ 0.9749; 0.9960] 1.9 2.2
## JohnsonEA04C 0.9990 [ 0.9975; 0.9996] 1.9 2.2
## JohnsonNijenhuisBouchard08A 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## JohnsonNijenhuisBouchard08A 0.8900 [ 0.7515; 0.9534] 2.0 2.2
## JohnsonNijenhuisBouchard08B 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## JohnsonNijenhuisBouchard08C 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## JohnsonNijenhuisBouchard08D 0.8100 [ 0.5926; 0.9174] 2.0 2.2
## JohnsonNijenhuisBouchard08E 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## JohnsonNijenhuisBouchard08F 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## JohnsonNijenhuisBouchard08G 0.7300 [ 0.4489; 0.8796] 2.0 2.2
## JohnsonNijenhuisBouchard08H 0.9300 [ 0.8376; 0.9707] 2.0 2.2
## JohnsonNijenhuisBouchard08I 0.9990 [ 0.9976; 0.9996] 2.0 2.2
## FloydEA10 0.9990 [ 0.9956; 0.9998] 0.7 2.0
## KaufmanEA12A 0.8600 [ 0.7650; 0.9184] 5.0 2.2
## KaufmanEA12B 0.8000 [ 0.6963; 0.8710] 7.1 2.2
## FloydEA12A 0.9700 [ 0.9061; 0.9906] 1.2 2.1
## FloydEA12B 0.9500 [ 0.8297; 0.9860] 1.0 2.1
## FloydEA12C 0.9990 [ 0.9962; 0.9997] 0.9 2.1
## FloydEA12D 0.8900 [ 0.6162; 0.9719] 0.8 2.0
## FloydEA12E 0.9200 [ 0.6619; 0.9831] 0.6 2.0
## Salthouse13 0.9100 [ 0.6399; 0.9800] 0.7 2.0
## ValeriusSparfeldt14A 0.9200 [ 0.8205; 0.9654] 2.2 2.2
## ValeriusSparfeldt14B 0.9900 [ 0.9765; 0.9958] 2.2 2.2
## ValeriusSparfeldt14C 0.9500 [ 0.8856; 0.9786] 2.2 2.2
## QuirogaEA15 0.9300 [ 0.7759; 0.9794] 1.0 2.1
## SwagermanEA16 0.9990 [ 0.9970; 0.9997] 1.3 2.1
## Lim88 0.9000 [ 0.7681; 0.9586] 1.9 2.2
##
## Number of studies combined: k = 47
##
## COR 95%-CI z p-value
## Fixed effect model 0.9718 [0.9680; 0.9751] 65.57 0
## Random effects model 0.9856 [0.9729; 0.9923] 15.19 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 1.1607 [0.7761; 1.8704]; tau = 1.0773 [0.8809; 1.3676];
## I^2 = 95.7% [94.9%; 96.4%]; H = 4.82 [4.43; 5.24]
##
## Test of heterogeneity:
## Q d.f. p-value
## 1067.88 46 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Fisher's z transformation of correlations#Forest plots
RAW <- forest(RCOR,
sortvar = TE,
xlim = c(-1, 1),
rightlabs = c("Correlation", "95% CI", "Weight"),
leftcols = c("Source"),
leftlabs = c("Study"),
pooled.totals = F,
smlab = "",
text.random = "Overall Effect",
print.tau2 = F,
col.diamond = "orangered",
col.diamond.lines = "black",
col.predict = "black",
print.I2.ci = F,
digits.sd = 2,
comb.fixed = F,
col.square = "#00348E",
overall = T)
STAND <- forest(ZCOR,
sortvar = TE,
xlim = c(-1, 1),
rightlabs = c("Correlation", "95% CI", "Weight"),
leftcols = c("Source"),
leftlabs = c("Study"),
pooled.totals = F,
smlab = "",
text.random = "Overall Effect",
print.tau2 = F,
col.diamond = "gold",
col.diamond.lines = "black",
col.predict = "black",
print.I2.ci = F,
digits.sd = 2,
comb.fixed = F,
col.square = "#5F85E7",
overall = T)
#Trim-and-fill
trimfill(RCOR); trimfill(ZCOR)## COR 95%-CI %W(random)
## Stone 92 0.9990 [ 0.9977; 1.0003] 1.8
## ByrdBuckhalt91 0.9990 [ 0.9974; 1.0006] 1.8
## TirreField2002A 0.9990 [ 0.9981; 0.9999] 1.8
## TirreField2002B 0.8900 [ 0.7942; 0.9858] 1.4
## TirreField2002C 0.9810 [ 0.9599; 1.0021] 1.7
## WothkeEA91 0.9990 [ 0.9980; 1.0000] 1.8
## Williamson69 0.9990 [ 0.9979; 1.0001] 1.8
## Kettner76A 0.9490 [ 0.9003; 0.9977] 1.7
## Kettner76B 0.9990 [ 0.9980; 1.0000] 1.8
## Palmer90 0.9750 [ 0.9526; 0.9974] 1.7
## KranzlerJensen91 0.3680 [-0.1953; 0.9313] 0.2
## LuoThompsonDetterman03 0.8700 [ 0.7686; 0.9714] 1.4
## Carey92 0.8900 [ 0.8188; 0.9612] 1.6
## AbrahamsEA94 0.8610 [ 0.8087; 0.9133] 1.6
## WolfeEA95 0.8660 [ 0.8179; 0.9141] 1.7
## NaglieriJensen87 0.9990 [ 0.9979; 1.0001] 1.8
## Engelhardt18 0.9800 [ 0.9651; 0.9949] 1.7
## StaufferReeCarretta96 0.9940 [ 0.9882; 0.9998] 1.8
## KeithKranzlerFlanagan01 0.9800 [ 0.9571; 1.0029] 1.7
## JohnsonEA04A 0.9900 [ 0.9813; 0.9987] 1.8
## JohnsonEA04B 0.9900 [ 0.9813; 0.9987] 1.8
## JohnsonEA04C 0.9990 [ 0.9981; 0.9999] 1.8
## JohnsonNijenhuisBouchard08A 0.9990 [ 0.9982; 0.9998] 1.8
## JohnsonNijenhuisBouchard08A 0.8900 [ 0.8018; 0.9782] 1.5
## JohnsonNijenhuisBouchard08B 0.9990 [ 0.9982; 0.9998] 1.8
## JohnsonNijenhuisBouchard08C 0.9990 [ 0.9982; 0.9998] 1.8
## JohnsonNijenhuisBouchard08D 0.8100 [ 0.6642; 0.9558] 1.2
## JohnsonNijenhuisBouchard08E 0.9990 [ 0.9982; 0.9998] 1.8
## JohnsonNijenhuisBouchard08F 0.9990 [ 0.9982; 0.9998] 1.8
## JohnsonNijenhuisBouchard08G 0.7300 [ 0.5319; 0.9281] 0.9
## JohnsonNijenhuisBouchard08H 0.9300 [ 0.8727; 0.9873] 1.6
## JohnsonNijenhuisBouchard08I 0.9990 [ 0.9982; 0.9998] 1.8
## FloydEA10 0.9990 [ 0.9977; 1.0003] 1.8
## KaufmanEA12A 0.8600 [ 0.7872; 0.9328] 1.6
## KaufmanEA12B 0.8000 [ 0.7154; 0.8846] 1.5
## FloydEA12A 0.9700 [ 0.9380; 1.0020] 1.7
## FloydEA12B 0.9500 [ 0.8930; 1.0070] 1.6
## FloydEA12C 0.9990 [ 0.9978; 1.0002] 1.8
## FloydEA12D 0.8900 [ 0.7596; 1.0204] 1.2
## FloydEA12E 0.9200 [ 0.8143; 1.0257] 1.4
## Salthouse13 0.9100 [ 0.7943; 1.0257] 1.3
## ValeriusSparfeldt14A 0.9200 [ 0.8568; 0.9832] 1.6
## ValeriusSparfeldt14B 0.9900 [ 0.9818; 0.9982] 1.8
## ValeriusSparfeldt14C 0.9500 [ 0.9099; 0.9901] 1.7
## QuirogaEA15 0.9300 [ 0.8532; 1.0068] 1.5
## SwagermanEA16 0.9990 [ 0.9980; 1.0000] 1.8
## Lim88 0.9000 [ 0.8176; 0.9824] 1.5
## Filled: JohnsonNijenhuisBouchard08H 1.0679 [ 1.0106; 1.1252] 1.6
## Filled: QuirogaEA15 1.0679 [ 0.9911; 1.1447] 1.5
## Filled: FloydEA12E 1.0779 [ 0.9722; 1.1836] 1.4
## Filled: ValeriusSparfeldt14A 1.0779 [ 1.0147; 1.1411] 1.6
## Filled: Salthouse13 1.0879 [ 0.9723; 1.2036] 1.3
## Filled: Lim88 1.0979 [ 1.0155; 1.1803] 1.5
## Filled: TirreField2002B 1.1079 [ 1.0121; 1.2037] 1.4
## Filled: Carey92 1.1079 [ 1.0367; 1.1791] 1.6
## Filled: JohnsonNijenhuisBouchard08A 1.1079 [ 1.0197; 1.1961] 1.5
## Filled: FloydEA12D 1.1079 [ 0.9775; 1.2383] 1.2
## Filled: LuoThompsonDetterman03 1.1279 [ 1.0265; 1.2293] 1.4
## Filled: WolfeEA95 1.1319 [ 1.0838; 1.1800] 1.7
## Filled: AbrahamsEA94 1.1369 [ 1.0846; 1.1892] 1.6
## Filled: KaufmanEA12A 1.1379 [ 1.0651; 1.2107] 1.6
## Filled: JohnsonNijenhuisBouchard08D 1.1879 [ 1.0421; 1.3337] 1.2
## Filled: KaufmanEA12B 1.1979 [ 1.1133; 1.2825] 1.5
## Filled: JohnsonNijenhuisBouchard08G 1.2679 [ 1.0698; 1.4660] 0.9
## Filled: KranzlerJensen91 1.6299 [ 1.0666; 2.1932] 0.2
##
## Number of studies combined: k = 65 (with 18 added studies)
##
## COR 95%-CI z p-value
## Random effects model 0.9941 [0.9670; 1.0212] 71.84 0
##
## Quantifying heterogeneity:
## tau^2 = 0.0109 [0.0048; 0.0140]; tau = 0.1045 [0.0695; 0.1182];
## I^2 = 82.9% [78.7%; 86.2%]; H = 2.42 [2.17; 2.69]
##
## Test of heterogeneity:
## Q d.f. p-value
## 373.40 64 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Trim-and-fill method to adjust for funnel plot asymmetry
## - Untransformed correlations## COR 95%-CI %W(random)
## Stone 92 0.9990 [ 0.9959; 0.9998] 1.6
## ByrdBuckhalt91 0.9990 [ 0.9925; 0.9999] 1.5
## TirreField2002A 0.9990 [ 0.9973; 0.9996] 1.6
## TirreField2002B 0.8900 [ 0.7322; 0.9571] 1.6
## TirreField2002C 0.9810 [ 0.9367; 0.9944] 1.6
## WothkeEA91 0.9990 [ 0.9969; 0.9997] 1.6
## Williamson69 0.9990 [ 0.9968; 0.9997] 1.6
## Kettner76A 0.9490 [ 0.8613; 0.9818] 1.6
## Kettner76B 0.9990 [ 0.9972; 0.9996] 1.6
## Palmer90 0.9750 [ 0.9360; 0.9904] 1.6
## KranzlerJensen91 0.3680 [-0.3382; 0.8091] 1.6
## LuoThompsonDetterman03 0.8700 [ 0.7141; 0.9437] 1.6
## Carey92 0.8900 [ 0.7889; 0.9442] 1.6
## AbrahamsEA94 0.8610 [ 0.7979; 0.9054] 1.6
## WolfeEA95 0.8660 [ 0.8084; 0.9072] 1.6
## NaglieriJensen87 0.9990 [ 0.9966; 0.9997] 1.6
## Engelhardt18 0.9800 [ 0.9569; 0.9908] 1.6
## StaufferReeCarretta96 0.9940 [ 0.9832; 0.9979] 1.6
## KeithKranzlerFlanagan01 0.9800 [ 0.9302; 0.9944] 1.6
## JohnsonEA04A 0.9900 [ 0.9749; 0.9960] 1.6
## JohnsonEA04B 0.9900 [ 0.9749; 0.9960] 1.6
## JohnsonEA04C 0.9990 [ 0.9975; 0.9996] 1.6
## JohnsonNijenhuisBouchard08A 0.9990 [ 0.9976; 0.9996] 1.6
## JohnsonNijenhuisBouchard08A 0.8900 [ 0.7515; 0.9534] 1.6
## JohnsonNijenhuisBouchard08B 0.9990 [ 0.9976; 0.9996] 1.6
## JohnsonNijenhuisBouchard08C 0.9990 [ 0.9976; 0.9996] 1.6
## JohnsonNijenhuisBouchard08D 0.8100 [ 0.5926; 0.9174] 1.6
## JohnsonNijenhuisBouchard08E 0.9990 [ 0.9976; 0.9996] 1.6
## JohnsonNijenhuisBouchard08F 0.9990 [ 0.9976; 0.9996] 1.6
## JohnsonNijenhuisBouchard08G 0.7300 [ 0.4489; 0.8796] 1.6
## JohnsonNijenhuisBouchard08H 0.9300 [ 0.8376; 0.9707] 1.6
## JohnsonNijenhuisBouchard08I 0.9990 [ 0.9976; 0.9996] 1.6
## FloydEA10 0.9990 [ 0.9956; 0.9998] 1.6
## KaufmanEA12A 0.8600 [ 0.7650; 0.9184] 1.6
## KaufmanEA12B 0.8000 [ 0.6963; 0.8710] 1.6
## FloydEA12A 0.9700 [ 0.9061; 0.9906] 1.6
## FloydEA12B 0.9500 [ 0.8297; 0.9860] 1.6
## FloydEA12C 0.9990 [ 0.9962; 0.9997] 1.6
## FloydEA12D 0.8900 [ 0.6162; 0.9719] 1.6
## FloydEA12E 0.9200 [ 0.6619; 0.9831] 1.5
## Salthouse13 0.9100 [ 0.6399; 0.9800] 1.5
## ValeriusSparfeldt14A 0.9200 [ 0.8205; 0.9654] 1.6
## ValeriusSparfeldt14B 0.9900 [ 0.9765; 0.9958] 1.6
## ValeriusSparfeldt14C 0.9500 [ 0.8856; 0.9786] 1.6
## QuirogaEA15 0.9300 [ 0.7759; 0.9794] 1.6
## SwagermanEA16 0.9990 [ 0.9970; 0.9997] 1.6
## Lim88 0.9000 [ 0.7681; 0.9586] 1.6
## Filled: ByrdBuckhalt91 -0.5451 [-0.9245; 0.3769] 1.5
## Filled: TirreField2002A -0.5451 [-0.8059; -0.1072] 1.6
## Filled: WothkeEA91 -0.5451 [-0.8253; -0.0494] 1.6
## Filled: Williamson69 -0.5451 [-0.8332; -0.0242] 1.6
## Filled: Kettner76B -0.5451 [-0.8126; -0.0879] 1.6
## Filled: NaglieriJensen87 -0.5451 [-0.8419; 0.0049] 1.6
## Filled: JohnsonEA04C -0.5451 [-0.7913; -0.1468] 1.6
## Filled: JohnsonNijenhuisBouchard08A -0.5451 [-0.7844; -0.1644] 1.6
## Filled: JohnsonNijenhuisBouchard08B -0.5451 [-0.7844; -0.1644] 1.6
## Filled: JohnsonNijenhuisBouchard08C -0.5451 [-0.7844; -0.1644] 1.6
## Filled: JohnsonNijenhuisBouchard08E -0.5451 [-0.7844; -0.1644] 1.6
## Filled: JohnsonNijenhuisBouchard08F -0.5451 [-0.7844; -0.1644] 1.6
## Filled: JohnsonNijenhuisBouchard08I -0.5451 [-0.7844; -0.1644] 1.6
## Filled: FloydEA10 -0.5451 [-0.8746; 0.1287] 1.6
## Filled: FloydEA12C -0.5451 [-0.8562; 0.0562] 1.6
## Filled: SwagermanEA16 -0.5451 [-0.8216; -0.0610] 1.6
##
## Number of studies combined: k = 63 (with 16 added studies)
##
## COR 95%-CI z p-value
## Random effects model 0.9338 [0.8560; 0.9702] 8.09 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 2.6605 [1.9016; 3.9538]; tau = 1.6311 [1.3790; 1.9884];
## I^2 = 97.5% [97.1%; 97.8%]; H = 6.28 [5.91; 6.68]
##
## Test of heterogeneity:
## Q d.f. p-value
## 2447.75 62 0
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Trim-and-fill method to adjust for funnel plot asymmetry
## - Fisher's z transformation of correlations#Funnel plots
dfR <- data.frame(RCOR$seTE, RCOR$TE); dfR$se <- dfR$RCOR.seTE; dfR$r <- dfR$RCOR.TE
dfZ <- data.frame(ZCOR$seTE, ZCOR$TE); dfZ$se <- FisherZInv(dfZ$ZCOR.seTE); dfZ$r <- FisherZInv(dfZ$ZCOR.TE)
estimateT = FisherZInv(ZCOR$TE.random); set = FisherZInv(ZCOR$seTE.random); estimateT## [1] 0.9855728estimateT2 = RCOR$TE.random; set2 = RCOR$seTE.random; estimateT2## [1] 0.9580958dfR; dfZse.seq = seq(0, max(dfZ$se), 0.001)
ll95 = estimateT - (1.96*se.seq)
ul95 = estimateT + (1.96*se.seq)
ll95a = FisherZInv(ZCOR$lower.random)
ul95a = FisherZInv(ZCOR$upper.random)
ll99 = estimateT - (3.29*se.seq)
ul99 = estimateT + (3.29*se.seq)
ll99a = 1.67857*FisherZInv(ZCOR$lower.random)
ul99a = 1.67857*FisherZInv(ZCOR$upper.random)
meanll95 = estimateT - (1.96*set)
meanul95 = estimateT + (1.96*set)
dfZCI <- data.frame(ll95, ul95, ll99, ul99, se.seq, estimateT, meanll95, meanul95, ll95a, ul95a, ll99a, ul99a)
se.seq2 = seq(0, max(dfR$se), 0.001)
ll952 = estimateT2 - (1.96*se.seq2)
ul952 = estimateT2 + (1.96*se.seq2)
ll952a = RCOR$lower.random
ul952a = RCOR$upper.random
ll992 = estimateT2 - (3.29*se.seq2)
ul992 = estimateT2 + (3.29*se.seq2)
ll992a = 1.67857*(RCOR$lower.random)
ul992a = 1.67857*(RCOR$upper.random)
meanll952 = estimateT2 - (1.96*set2)
meanul952 = estimateT2 + (1.96*set2)
dfRCI <- data.frame(ll952, ul952, ll992, ul992, se.seq2, estimateT2, meanll952, meanul952, ll952a, ul952a, ll992a, ul992a)
STAND <- ggplot(aes(x = se, y = r), data = dfZ) +
geom_point(shape = 16, size = 3, colour = "#00348E") +
xlab('Standard Error') + ylab('r-to-z Correlations') +
geom_line(aes(x = se.seq, y = ll95), linetype = 'dotted', colour = "#666666", size = 1, data = dfZCI) +
geom_line(aes(x = se.seq, y = ul95), linetype = 'dotted', colour = "#666666", size = 1, data = dfZCI) +
geom_line(aes(x = se.seq, y = ll99), linetype = 'dashed', colour = "#666666", size = 1, data = dfZCI) +
geom_line(aes(x = se.seq, y = ul99), linetype = 'dashed', colour = "#666666", size = 1, data = dfZCI) +
geom_segment(aes(x = min(se.seq), y = estimateT, xend = max(se.seq), yend = estimateT), linetype='dotted', colour = "#E9C535", size = 1, data=dfZCI) +
geom_segment(aes(x = min(se.seq), y = ll95a, xend = max(se.seq), yend = ll95a), linetype='dotted' , colour = "gold", size = 1, data=dfZCI) +
geom_segment(aes(x = min(se.seq), y = ul95a, xend = max(se.seq), yend = ul95a), linetype='dotted' , colour = "gold", size = 1, data=dfZCI) +
scale_x_reverse() +
coord_flip() +
theme_bw() +
theme(text = element_text(family = "serif", size = 12))
RAW <- ggplot(aes(x = se, y = r), data = dfR) +
geom_point(shape = 16, size = 3, colour = "#5F85E7") +
xlab('Standard Error') + ylab('Raw Correlations') +
geom_line(aes(x = se.seq2, y = ll952), linetype = 'dotted', colour = "#666666", size = 1, data = dfRCI) +
geom_line(aes(x = se.seq2, y = ul952), linetype = 'dotted', colour = "#666666", size = 1, data = dfRCI) +
geom_line(aes(x = se.seq2, y = ll992), linetype = 'dashed', colour = "#666666", size = 1, data = dfRCI) +
geom_line(aes(x = se.seq2, y = ul992), linetype = 'dashed', colour = "#666666", size = 1, data = dfRCI) +
geom_segment(aes(x = min(se.seq2), y = estimateT2, xend = max(se.seq2), yend = estimateT2), linetype='dotted', colour = "#E9C535", size = 1, data=dfRCI) +
geom_segment(aes(x = min(se.seq2), y = ll952a, xend = max(se.seq2), yend = ll952a), linetype='dotted' , colour = "gold", size = 1, data=dfRCI) +
geom_segment(aes(x = min(se.seq2), y = ul952a, xend = max(se.seq2), yend = ul952a), linetype='dotted' , colour = "gold", size = 1, data=dfRCI) +
scale_x_reverse() +
coord_flip() +
theme_bw() +
theme(text = element_text(family = "serif", size = 12))
RAW; STAND
multiplot(RAW, STAND, cols = 2)
Conclusions
The relationship between the g factors from various tests is consistent with identity (meta-analytic r = 0.99). There is extremely limited discriminant validity for the g factors from different tests, suggesting a reflective phenotypic model is appropriate. On the other hand, a formative model is difficult to justify. The indifference of the indicator is an exceptionally robust phenomenon that persists despite a diversity of test content, modality, and sample age. Practitioners can be confident that their tests will be reasonably interchangeable for the general population; furthermore, the use of different tests will - for the most part - not assess different constructs barring failures of invariance, as in illiterate or blind samples. This finding is perhaps trivial to intelligence researchers, but systematic proof was lacking before this analysis; the indifference of the indicator and its not-so-necessary corollary of the identity of g factors from different cognitive tests - regardless of content -, which was strongly evidenced before, can now be reasonably taken for granted.
Sources
- To-do
To-do
- Add Snow et al. (1977), Woodcock (1978), and McGrew & Woodcock (2001).
- Analyze the other methods used and manifest dimensionality
- Assess heterogeneity by age and test combination/model/battery size and representativeness (new columns required)
- Additional plots with test combination groupings, among others