Za ilustraciju jackknife procedure iskoristićemo eksperiment o uticaju socijalnog isključivanja na perifernu temperaturu. Originalna studija IJzerman et al. (2012) (https://doi.org/10.1016/j.actpsy.2012.05.002) je pokazala da telesna temperatura ispitanika (merena na prstu) opada u eksperimentalnoj situaciji socijalnog isključivanja, dok kod grupe koja je uključena nema promene u temperaturi. Trenutno je u planu velika replikaciona studija koja će pokušati da potvrdi ili opovrgne ovaj efekat u većem broju nezavisnih laboratorija (https://osf.io/v5s6d/). Za potrebe nove studije kreirali smo skript koji sadrži konfirmatorne analize, uključujući i jackknife postupak. Ovde je izdvojen jedan deo tog skripta.
paket faux služi generisanju baza podataka koje imaju višeslojnu
strukturu
paket dyplyr služi lakšoj manipulaciji podacima
paket lme4 služi modelovanju mešovitih modela
paket pbkrtest služi poređenju fita mešovitih modela
library(faux)
library(dplyr)
library(lme4)
library(pbkrtest)Kreiraćemo mali uzorak da bi se analize izvele relativno brzo.
Na početku postavljamo seed da bismo uvek dobili iste rezultate kada
pokrenemo skript.
set.seed(2345)
d <- add_random(lab = 3) %>%
add_random(ID = round(runif(3, min=10, max=20)), .nested_in = "lab") %>%
add_random(point = 15) %>%
add_between("ID", condition = c("inclusion","exclusion")) %>%
add_recode("condition", "Condition", inclusion = 0, exclusion = 1) %>%
add_ranef("ID", temp_baseline = 0.5) %>%
mutate(temp_baseline = 35 + temp_baseline) %>%
add_ranef("point", temp_actual = 0.5, t_slope = 0.5, .cors = 0) %>%
add_ranef(sigma = 1) %>%
mutate(temp_actual = 35 + temp_actual + (0 + t_slope) * Condition + sigma) %>%
add_between("point", tik = 0:14) %>%
add_ranef(c("ID","point"), t = 1) %>%
mutate(t = as.numeric(tik) * 10 + t)
d$temp <- d$temp_actual - d$temp_baseline # deviation of actual temperature from a person's baseline temperature
d$time <- round(d$t/10 - 0.49, 0) # rounding time to multiple of 10 (fully elapsed) seconds
d <- mutate(d, time = ifelse(time < 0, 0, time)) # transforming negative values to 0
d$condition_ref_zero <- d$Condition - 0.5 # centering the condition variable, i.e. zero as the reference group
d$condition_ref_included <- d$Condition # using the included group as the reference group
d$condition_ref_excluded <- d$Condition - 1 # using the excluded group as the reference group
d$time_ref_0 <- d$time - 18 # centering the time variable around the midpoint (180s)
d$time_ref_max <- d$time - 36 # centering the time variable around it's maximum value (360s)U pitanju je generalni mešani model (general mixed model) gde je periferna temperatura na kažiprstu zavisna varijabla, a prediktori su vreme merenja (kontinuirani prediktor), eksperimentalna manipulacija (isključenost vs. uključnenost) i njihova interakcija. Kako je struktura podataka višeslojna (multilevel) - mere temperature su ugnježdene u ispitanike, pored fiksnih faktora, u model uključujemo i slučajne faktore. Jedan slučajni faktor odnosi se na intercept za ispitanike (nemaju svi istu prosečnu temperaturu), a drugi na efekat vremena na temperaturu (kod različitih ispitanika promene u temperaturi mogu biti različite brzine). Na kraju, kako postoji još jedan nivo ugnježdavanja - ispitanici su ugnježdeni u laboratorije - uključujemo i slučajan efekat laboratorije u model.
Glavna istraživačka hipoteza tiče se efekta interakcije vremena i eksperimentalne grupe. Kako bismo procenili njenu značajnost, pravimo dva modela - glavni istraživački model i model za poređenje. Model za poređenje je isti kao i istraživački, osim što ne sadrži interkaciju. Poređenjem fita ova dva modela dobijamo procenu veličine i značajnosti efekta.
Istraživački model
m1<- lmer(temp ~ (time | ID) + time + condition_ref_zero + time:condition_ref_zero + (1 | lab), data=d)## boundary (singular) fit: see help('isSingular')summary(m1)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## temp ~ (time | ID) + time + condition_ref_zero + time:condition_ref_zero +
## (1 | lab)
## Data: d
##
## REML criterion at convergence: 1912.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0896 -0.6457 0.0280 0.6004 3.3986
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 2.539e-01 0.503898
## time 1.089e-05 0.003301 -1.00
## lab (Intercept) 8.336e-02 0.288722
## Residual 1.265e+00 1.124548
## Number of obs: 600, groups: ID, 40; lab, 3
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.03658 0.20691 -0.177
## time 0.01672 0.01053 1.588
## condition_ref_zero -0.31016 0.24348 -1.274
## time:condition_ref_zero 0.02990 0.02106 1.420
##
## Correlation of Fixed Effects:
## (Intr) time cndt__
## time -0.404
## cndtn_rf_zr 0.001 0.006
## tm:cndtn_r_ 0.003 -0.008 -0.686
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Model za poređenje i poređenje dva modela
m0<- lmer(temp ~ (time | ID) + time + condition_ref_zero + (1 | lab), data=d)## boundary (singular) fit: see help('isSingular')KRmodcomp(m1, m0)## large : temp ~ (time | ID) + time + condition_ref_zero + time:condition_ref_zero +
## (1 | lab)
## small : temp ~ (time | ID) + time + condition_ref_zero + (1 | lab)
## stat ndf ddf F.scaling p.value
## Ftest 2.0151 1.0000 37.8771 1 0.1639Pošto smo generisali jako mali uzorak (za kompleksnu strukturu podataka) i slučajan - efekat nije značajan, ali to zanemarujemo.
Da bismo proverili da li su rezultati osetljivi na outliere koristimo jackknife.
Prvo, pravimo funkciju koja (iz prethodnog outputa) izvlači i prikazuje samo značajnost interakcije.
get_p <- function(d) {
m1<- lmer(temp ~ (time | ID) + time + condition_ref_zero + time:condition_ref_zero + (1 | lab), data=d)
m0<- lmer(temp ~ (time | ID) + time + condition_ref_zero + (1 | lab), data=d)
k<-KRmodcomp(m1, m0)
p=k$stats['p.value']
p
}Zatim, kreiramo funkciju koja isključuje samo po jednog ispitanika iz uzorka u datom trenutku, za sve ispitanike. Drugim rečima, kreiramo N uzoraka čija je veličina N-1 (i svi su različiti jer se svaki put isključuje drugi ispitanik iz uzorka) - jackknife postupak.
unique(d$ID) # original sample - unique participant IDs## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36"
## [37] "I37" "I38" "I39" "I40"# jackknifed subsamples - unique participant IDs
for (i in unique(d$ID)) {
dd <- d[which(d$ID!=i),]
print(unique(dd$ID))
}## [1] "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I06" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I07" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I08" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I09" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I10" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I11" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I12" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I13"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I18" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I19" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I20" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I21" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I22" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I23" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I24" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I25"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I30" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I31" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I32" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I33" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I34" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I35" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I36" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I37"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36"
## [37] "I38" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36"
## [37] "I37" "I39" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36"
## [37] "I37" "I38" "I40"
## [1] "I01" "I02" "I03" "I04" "I05" "I06" "I07" "I08" "I09" "I10" "I11" "I12"
## [13] "I13" "I14" "I15" "I16" "I17" "I18" "I19" "I20" "I21" "I22" "I23" "I24"
## [25] "I25" "I26" "I27" "I28" "I29" "I30" "I31" "I32" "I33" "I34" "I35" "I36"
## [37] "I37" "I38" "I39"Na kraju, koristimo jackknife postupak da procenimo da li su rezultati osetljivi na outliere tako što poredimo originalni rezultat sa rezultatima dobijenim na jackknife poduzorcima.
# p-value for the original sample
res <- cbind(out='none', pvalue=get_p(d))
print(res)## out pvalue
## p.value "none" 0.1639145# p-values for the jackknifed subsamples
for (i in unique(d$ID)) {
dd<-d[which(d$ID!=i),]
string <- paste('case ',i)
res <- cbind(out=string, pvalue=get_p(dd))
print(res)
}## out pvalue
## p.value "case I01" 0.1654442
## out pvalue
## p.value "case I02" 0.1879651
## out pvalue
## p.value "case I03" 0.1183316
## out pvalue
## p.value "case I04" 0.133608
## out pvalue
## p.value "case I05" 0.2197063
## out pvalue
## p.value "case I06" 0.1480865
## out pvalue
## p.value "case I07" 0.1473975
## out pvalue
## p.value "case I08" 0.180371
## out pvalue
## p.value "case I09" 0.1751511
## out pvalue
## p.value "case I10" 0.2295616
## out pvalue
## p.value "case I11" 0.1418814
## out pvalue
## p.value "case I12" 0.1964088
## out pvalue
## p.value "case I13" 0.2009045
## out pvalue
## p.value "case I14" 0.2132399
## out pvalue
## p.value "case I15" 0.2396534
## out pvalue
## p.value "case I16" 0.1509657
## out pvalue
## p.value "case I17" 0.208867
## out pvalue
## p.value "case I18" 0.2181665
## out pvalue
## p.value "case I19" 0.1456761
## out pvalue
## p.value "case I20" 0.124382
## out pvalue
## p.value "case I21" 0.1119768
## out pvalue
## p.value "case I22" 0.2258116
## out pvalue
## p.value "case I23" 0.2362346
## out pvalue
## p.value "case I24" 0.1539123
## out pvalue
## p.value "case I25" 0.1695453
## out pvalue
## p.value "case I26" 0.2663642
## out pvalue
## p.value "case I27" 0.125205
## out pvalue
## p.value "case I28" 0.1119671
## out pvalue
## p.value "case I29" 0.2135189
## out pvalue
## p.value "case I30" 0.1325667
## out pvalue
## p.value "case I31" 0.1775405
## out pvalue
## p.value "case I32" 0.3678118
## out pvalue
## p.value "case I33" 0.1638288
## out pvalue
## p.value "case I34" 0.1410615
## out pvalue
## p.value "case I35" 0.1438598
## out pvalue
## p.value "case I36" 0.1928798
## out pvalue
## p.value "case I37" 0.2408546
## out pvalue
## p.value "case I38" 0.1163684
## out pvalue
## p.value "case I39" 0.1338896
## out pvalue
## p.value "case I40" 0.09754535