#################################################################
# #
# Analysis for "What would disprove interdependence? #
# Lessons learned from a study on biliteracy in Portuguese #
# heritage language speakers in Switzerland" #
# #
# Raphael Berthele (raphael.berthele@unifr.ch) #
# Jan Vanhove (jan.vanhove@unifr.ch) #
# #
#################################################################
# Load packages
library(tidyverse) # for working with dataframes
## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr
## Conflicts with tidy packages ----------------------------------------------
## filter(): dplyr, stats
## lag(): dplyr, stats
library(cowplot) # additional plotting functionality
##
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggplot2':
##
## ggsave
library(lme4) # mixed-effects modelling
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
##
## expand
# Set plotting theme
theme_set(theme_cowplot(11))
# Read in and recode data
# Two arrangments of same data
reading_melt <- read.csv("Data/reading_melt.csv")
reading2_23 <- read.csv("Data/reading2_23.csv")
# Code Time as factor
reading_melt$Time <- factor(reading_melt$Time)
reading2_23$Time <- factor(reading2_23$Time)
# Multiply all values by 100 (percentages rather than proportions)
reading_melt$value <- 100 * reading_melt$value
reading2_23$value <- 100 * reading2_23$value
reading2_23$PreviousOther <- 100 * reading2_23$PreviousOther
reading2_23$PreviousSame <- 100 * reading2_23$PreviousSame
reading2_23$PreviousSchool <- 100 * reading2_23$PreviousSchool
reading2_23$PreviousPortuguese <- 100 * reading2_23$PreviousPortuguese
# More comprehensible labels for the language groups
reading_melt$BilingualControl2 <- reading_melt$LanguageGroup2
levels(reading_melt$BilingualControl2) <- c("bilingual (French)",
"bilingual (German)",
"comparison",
"comparison",
"comparison")
# Figure 1: Boxplot reading comprehension scores
language_names <- c(
`French` = "tested in French",
`German` = "tested in German",
`Portuguese` = "tested in Portuguese"
)
# function for number of observations
give.n <- function(x, add = 3){
return(c(y = median(x) + add, label = length(x)))
# experiment with the add parameter to find the perfect position
}
ggplot(reading_melt, aes(Time, value, fill = BilingualControl2)) +
geom_boxplot(outlier.shape = 1) +
facet_wrap(~ LanguageTested2,
labeller = as_labeller(language_names)) +
stat_summary(fun.data = give.n, geom = "text",
fun.y = median, size = 2.5,
position = position_dodge(width = 0.75)) +
xlab("Time of data collection") +
ylab("Reading score") +
theme(legend.direction = "horizontal",
legend.position = "bottom",
strip.text.x = element_text(size = 11),
panel.grid = element_blank(),
panel.grid.major.y = element_line(colour = "grey90"),
axis.text = element_text(colour = "black")) +
scale_fill_grey(start = 0.4, end = 1) +
labs(fill = "Bilingual vs. comparison")
# The corresponding table with means, ns and standard deviations
reading_melt %>%
group_by(Time, BilingualControl2, LanguageTested2) %>%
summarise(n = n(),
mean = mean(value),
sd = sd(value)) %>%
print(n = nrow(.))
## Source: local data frame [21 x 6]
## Groups: Time, BilingualControl2 [?]
##
## Time BilingualControl2 LanguageTested2 n mean sd
## <fctr> <fctr> <fctr> <int> <dbl> <dbl>
## 1 1 bilingual (French) French 106 57.24926 16.81236
## 2 1 bilingual (French) Portuguese 104 53.28947 20.10766
## 3 1 bilingual (German) German 105 45.01253 17.86287
## 4 1 bilingual (German) Portuguese 104 46.25506 20.09408
## 5 1 comparison French 75 56.21053 23.82462
## 6 1 comparison German 78 51.14710 17.60771
## 7 1 comparison Portuguese 74 67.85206 17.90804
## 8 2 bilingual (French) French 107 65.12543 17.80460
## 9 2 bilingual (French) Portuguese 105 65.21303 19.95487
## 10 2 bilingual (German) German 92 54.91991 18.20378
## 11 2 bilingual (German) Portuguese 97 55.34455 15.77326
## 12 2 comparison French 75 68.56140 18.81758
## 13 2 comparison German 79 65.75616 17.81584
## 14 2 comparison Portuguese 75 77.89474 17.39147
## 15 3 bilingual (French) French 102 72.96182 17.05119
## 16 3 bilingual (French) Portuguese 105 73.83459 17.47814
## 17 3 bilingual (German) German 90 65.08772 18.18853
## 18 3 bilingual (German) Portuguese 93 66.04414 18.02477
## 19 3 comparison French 71 75.90808 16.84826
## 20 3 comparison German 75 73.54386 16.50746
## 21 3 comparison Portuguese 69 83.75286 12.36757
# Figure 2: Scatterplot with school language on x-axis
theme_set(theme_bw(10))
labels <- c(
`French` = "tested in French",
`German` = "tested in German",
`Portuguese` = "tested in Portuguese",
`Bilingual group (French)` = "Bilingual group (French)",
`Bilingual group (German)` = "Bilingual group (German)",
`2` = "T1-T2",
`3` = "T2-T3"
)
p <- ggplot(reading2_23, aes(x = PreviousSchool, y = value)) +
geom_point(shape = 1, position = position_jitter(0.8, 0.8)) +
stat_smooth(method = "lm", se = FALSE, colour = "black") +
facet_grid(Time ~ LanguageGroup2 + LanguageTested2,
labeller = as_labeller(labels)) +
ylab("Reading comprehension score") +
xlab("Previous score: School language") +
ggtitle("Reading comprehension score depending on previous school language score\n(participant group by time)") +
theme(legend.direction = "horizontal",
legend.position = "bottom",
strip.text.x = element_text(size = 11),
strip.text.y = element_text(size = 11),
panel.grid = element_blank(),
axis.text = element_text(colour = "black"))
# Compute correlations/n
n_r_reading_School <- summarise(group_by(reading2_23, Time, LanguageGroup2, LanguageTested2),
r = format(round(cor(PreviousSchool, value, use = "p"), 2), nsmall = 2),
n = length(PreviousPortuguese[!is.na(PreviousSchool) & !is.na(value)]))
# Combine both numbers into a text string
n_r_reading_School$Label <- paste("n = ", as.character(n_r_reading_School$n), ", r = ", as.character(n_r_reading_School$r), sep = "")
# Add x/y positions for text labels
n_r_reading_School$x <- 100; n_r_reading_School$y <- 0
# Draw graph
p + geom_text(aes(x, y, label = Label, group = NULL),
hjust = 1, vjust = 0, # vertical/horizontal adjustment for labels
size = 4,
data = n_r_reading_School)
## Warning: Removed 61 rows containing non-finite values (stat_smooth).
## Warning: Removed 61 rows containing missing values (geom_point).
# Figure 3: Scatterplot with heritage language on x-axis
theme_set(theme_bw(10))
p <- ggplot(reading2_23, aes(x = PreviousPortuguese, y = value)) +
geom_point(shape = 1, position = position_jitter(width = 0.8, height = 0.8)) +
stat_smooth(method = "lm", se = FALSE, colour = "black") +
facet_grid(Time ~ LanguageGroup2 + LanguageTested2,
labeller = as_labeller(labels)) +
ylab("Reading comprehension score") +
xlab("Previous score: Portuguese") +
ggtitle("Reading comprehension score depending on previous Portuguese score\n(participant group by time)") +
theme(legend.direction = "horizontal",
legend.position = "bottom",
strip.text.x = element_text(size = 11),
strip.text.y = element_text(size = 11),
panel.grid = element_blank(),
axis.text = element_text(colour = "black"))
# Compute correlations/n
n_r_reading_Port <- summarise(group_by(reading2_23, Time, LanguageGroup2, LanguageTested2),
r = format(round(cor(PreviousPortuguese, value, use = "p"), 2), nsmall = 2),
n = length(PreviousPortuguese[!is.na(PreviousPortuguese) & !is.na(value)]))
# Combine both numbers into a text string
n_r_reading_Port$Label <- paste("n = ", as.character(n_r_reading_Port$n), ", r = ", as.character(n_r_reading_Port$r), sep = "")
# Add x/y positions for text labels
n_r_reading_Port$x <- 100; n_r_reading_Port$y <- 0
# Draw graph
p + geom_text(aes(x, y, label = Label, group = NULL),
hjust = 1, vjust = 0, # vertical/horizontal adjustment for labels
size = 4,
data = n_r_reading_Port)
## Warning: Removed 74 rows containing non-finite values (stat_smooth).
## Warning: Removed 74 rows containing missing values (geom_point).
# Mixed model analyses
# Retain only variables of interest
reading2_23_complete <- reading2_23 %>%
select(VPNID, Class, Time, LanguageTested, LanguageGroup2,
PreviousSame, PreviousOther,
value)
reading2_23_complete <- reading2_23_complete[complete.cases(reading2_23_complete), ]
# Centre or sum-code variables
reading2_23_complete$n.Time <- as.numeric(reading2_23_complete$Time) - 1.5
reading2_23_complete$n.HL <- as.numeric(reading2_23_complete$LanguageTested) - 1.5
reading2_23_complete$n.German <- as.numeric(reading2_23_complete$LanguageGroup2) - 1.5
reading2_23_complete$c.PreviousSame <- (reading2_23_complete$PreviousSame - mean(reading2_23_complete$PreviousSame))/100
reading2_23_complete$c.PreviousOther <- (reading2_23_complete$PreviousOther - mean(reading2_23_complete$PreviousOther))/100
reading2_23_complete$value <- reading2_23_complete$value/100
# Dividing PreviousSame and PreviousOther by 100 again works better (better convergence).
# FIRST PREDICTION
# Null model for first prediction
reading.lmer1 <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
# add FE for PreviousOther
reading.lmer2 <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame + c.PreviousOther +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
# Model comparison: X²(1) = 10.7, p = 0.001
anova(reading.lmer1, reading.lmer2)
## refitting model(s) with ML (instead of REML)
## Data: reading2_23_complete
## Models:
## reading.lmer1: value ~ n.Time + n.HL * n.German + c.PreviousSame + (1 | VPNID) +
## reading.lmer1: (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class)
## reading.lmer2: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther +
## reading.lmer2: (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer2: n.HL | Class)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## reading.lmer1 23 -825.74 -721.73 435.87 -871.74
## reading.lmer2 24 -834.47 -725.94 441.23 -882.47 10.73 1 0.001054
##
## reading.lmer1
## reading.lmer2 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Estimates of beta coefficients:
summary(reading.lmer2)
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther +
## (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## n.HL | Class)
## Data: reading2_23_complete
##
## REML criterion at convergence: -837.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6301 -0.5968 0.0279 0.6108 2.6531
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## VPNID (Intercept) 0.0033746 0.05809
## Class (Intercept) 0.0008207 0.02865
## n.Time 0.0019298 0.04393 -0.49
## c.PreviousSame 0.0076691 0.08757 0.95 -0.73
## c.PreviousOther 0.0106184 0.10305 -0.89 0.84 -0.99
## n.HL 0.0002134 0.01461 0.79 0.14 0.57 -0.42
## Residual 0.0127648 0.11298
## Number of obs: 680, groups: VPNID, 206; Class, 21
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.655782 0.009243 70.95
## n.Time 0.021173 0.014450 1.47
## n.HL 0.009093 0.009613 0.95
## n.German -0.019474 0.016639 -1.17
## c.PreviousSame 0.469236 0.036935 12.70
## c.PreviousOther 0.159104 0.039735 4.00
## n.HL:n.German 0.004062 0.018879 0.22
##
## Correlation of Fixed Effects:
## (Intr) n.Time n.HL n.Grmn c.PrvS c.PrvO
## n.Time -0.247
## n.HL 0.222 0.046
## n.German -0.040 -0.030 -0.023
## c.PreviosSm 0.408 -0.444 0.148 0.038
## c.PrevsOthr -0.422 0.259 -0.131 0.172 -0.514
## n.HL:n.Grmn -0.038 -0.017 0.062 0.179 -0.059 0.051
# SECOND PREDICTION
# L1-to-L2 vs. L2-to-L1 effects
reading.lmer3 <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame + c.PreviousOther*n.HL +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
anova(reading.lmer2, reading.lmer3) # X² = 0.64, p = 0.42
## refitting model(s) with ML (instead of REML)
## Data: reading2_23_complete
## Models:
## reading.lmer2: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther +
## reading.lmer2: (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer2: n.HL | Class)
## reading.lmer3: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## reading.lmer3: n.HL + (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer3: n.HL | Class)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## reading.lmer2 24 -834.47 -725.94 441.23 -882.47
## reading.lmer3 25 -833.10 -720.05 441.55 -883.10 0.6375 1 0.4246
summary(reading.lmer3)
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## n.HL + (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## n.HL | Class)
## Data: reading2_23_complete
##
## REML criterion at convergence: -834.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6990 -0.5995 0.0247 0.6148 2.5890
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## VPNID (Intercept) 0.0032874 0.05734
## Class (Intercept) 0.0008632 0.02938
## n.Time 0.0019435 0.04408 -0.50
## c.PreviousSame 0.0077904 0.08826 0.95 -0.74
## c.PreviousOther 0.0110259 0.10500 -0.89 0.84 -0.99
## n.HL 0.0002362 0.01537 0.86 0.02 0.65 -0.53
## Residual 0.0128134 0.11320
## Number of obs: 680, groups: VPNID, 206; Class, 21
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.6562021 0.0093506 70.18
## n.Time 0.0208377 0.0144834 1.44
## n.HL 0.0094979 0.0096935 0.98
## n.German -0.0191137 0.0167389 -1.14
## c.PreviousSame 0.4723364 0.0370543 12.75
## c.PreviousOther 0.1567178 0.0401676 3.90
## n.HL:n.German 0.0004216 0.0195653 0.02
## n.HL:c.PreviousOther -0.0418490 0.0497620 -0.84
##
## Correlation of Fixed Effects:
## (Intr) n.Time n.HL n.Grmn c.PrvS c.PrvO n.HL:.G
## n.Time -0.252
## n.HL 0.253 0.015
## n.German -0.041 -0.030 -0.026
## c.PreviosSm 0.413 -0.448 0.171 0.038
## c.PrevsOthr -0.434 0.263 -0.161 0.169 -0.523
## n.HL:n.Grmn -0.045 -0.015 0.056 0.187 -0.069 0.073
## n.HL:c.PrvO -0.030 0.000 -0.012 -0.010 -0.048 0.090 0.242
# THIRD PREDICTION
reading.lmer4 <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame + c.PreviousOther*n.German +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
anova(reading.lmer2, reading.lmer4) # X² = 0.01, p = 0.93
## refitting model(s) with ML (instead of REML)
## Data: reading2_23_complete
## Models:
## reading.lmer2: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther +
## reading.lmer2: (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer2: n.HL | Class)
## reading.lmer4: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## reading.lmer4: n.German + (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer4: n.HL | Class)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## reading.lmer2 24 -834.47 -725.94 441.23 -882.47
## reading.lmer4 25 -832.47 -719.42 441.24 -882.47 0.0081 1 0.9284
summary(reading.lmer4)
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## n.German + (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## n.HL | Class)
## Data: reading2_23_complete
##
## REML criterion at convergence: -834.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6291 -0.5948 0.0281 0.6101 2.6527
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## VPNID (Intercept) 0.0034032 0.05834
## Class (Intercept) 0.0008337 0.02887
## n.Time 0.0019116 0.04372 -0.49
## c.PreviousSame 0.0074850 0.08652 0.95 -0.73
## c.PreviousOther 0.0113230 0.10641 -0.89 0.83 -0.99
## n.HL 0.0002143 0.01464 0.79 0.15 0.57 -0.42
## Residual 0.0127651 0.11298
## Number of obs: 680, groups: VPNID, 206; Class, 21
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.656111 0.009550 68.70
## n.Time 0.021363 0.014486 1.47
## n.HL 0.009127 0.009621 0.95
## n.German -0.020053 0.017301 -1.16
## c.PreviousSame 0.468869 0.037018 12.67
## c.PreviousOther 0.158194 0.040266 3.93
## n.HL:n.German 0.003981 0.018938 0.21
## n.German:c.PreviousOther 0.005635 0.069553 0.08
##
## Correlation of Fixed Effects:
## (Intr) n.Time n.HL n.Grmn c.PrvS c.PrvO n.HL:.
## n.Time -0.259
## n.HL 0.224 0.044
## n.German -0.097 -0.004 -0.030
## c.PreviosSm 0.416 -0.447 0.149 0.011
## c.PrevsOthr -0.423 0.262 -0.133 0.169 -0.513
## n.HL:n.Grmn -0.053 -0.010 0.059 0.192 -0.066 0.052
## n.Grmn:c.PO 0.232 -0.099 0.031 -0.263 0.105 -0.012 -0.076
# Follow-up analyses typological effect
# Interaction between PreviousOther, LanguageGroup2 and Time:
reading.lmer5 <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame + c.PreviousOther*n.German*n.Time +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
reading.lmer5_null <- lmer(value ~ n.Time + n.HL*n.German +
c.PreviousSame + c.PreviousOther*n.German + c.PreviousOther*n.Time + n.Time*n.German +
(1|VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther + n.HL | Class),
data = reading2_23_complete)
anova(reading.lmer5, reading.lmer5_null) # X² = 10.2, p = 0.001.
## refitting model(s) with ML (instead of REML)
## Data: reading2_23_complete
## Models:
## reading.lmer5_null: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## reading.lmer5_null: n.German + c.PreviousOther * n.Time + n.Time * n.German +
## reading.lmer5_null: (1 | VPNID) + (1 + n.Time + c.PreviousSame + c.PreviousOther +
## reading.lmer5_null: n.HL | Class)
## reading.lmer5: value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## reading.lmer5: n.German * n.Time + (1 | VPNID) + (1 + n.Time + c.PreviousSame +
## reading.lmer5: c.PreviousOther + n.HL | Class)
## Df AIC BIC logLik deviance Chisq Chi Df
## reading.lmer5_null 27 -830.55 -708.46 442.28 -884.55
## reading.lmer5 28 -838.73 -712.11 447.36 -894.73 10.173 1
## Pr(>Chisq)
## reading.lmer5_null
## reading.lmer5 0.001425 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(reading.lmer5)
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## value ~ n.Time + n.HL * n.German + c.PreviousSame + c.PreviousOther *
## n.German * n.Time + (1 | VPNID) + (1 + n.Time + c.PreviousSame +
## c.PreviousOther + n.HL | Class)
## Data: reading2_23_complete
##
## REML criterion at convergence: -834.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4064 -0.5613 0.0183 0.6208 2.5015
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## VPNID (Intercept) 0.0038244 0.06184
## Class (Intercept) 0.0007715 0.02778
## n.Time 0.0017848 0.04225 -0.45
## c.PreviousSame 0.0100025 0.10001 0.88 -0.58
## c.PreviousOther 0.0109259 0.10453 -0.91 0.77 -0.92
## n.HL 0.0003150 0.01775 0.63 0.26 0.63 -0.37
## Residual 0.0122855 0.11084
## Number of obs: 680, groups: VPNID, 206; Class, 21
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.655901 0.009505 69.00
## n.Time 0.031266 0.014421 2.17
## n.HL 0.007927 0.009872 0.80
## n.German -0.023212 0.017322 -1.34
## c.PreviousSame 0.465629 0.039393 11.82
## c.PreviousOther 0.164002 0.040441 4.06
## n.HL:n.German 0.007037 0.019359 0.36
## n.German:c.PreviousOther -0.006768 0.070397 -0.10
## n.Time:c.PreviousOther -0.058327 0.052631 -1.11
## n.Time:n.German -0.007198 0.026456 -0.27
## n.Time:n.German:c.PreviousOther 0.340088 0.104455 3.26
##
## Correlation of Fixed Effects:
## (Intr) n.Time n.HL n.Grmn c.PrvS c.PrvO n.HL:. n.G:.P n.T:.P
## n.Time -0.229
## n.HL 0.201 0.081
## n.German -0.087 -0.014 -0.015
## c.PreviosSm 0.413 -0.398 0.205 0.024
## c.PrevsOthr -0.423 0.235 -0.135 0.169 -0.497
## n.HL:n.Grmn -0.043 -0.024 0.051 0.128 -0.060 0.036
## n.Grmn:c.PO 0.221 -0.096 0.023 -0.273 0.076 -0.011 -0.044
## n.Tm:c.PrvO -0.098 0.019 -0.008 -0.034 -0.124 0.056 -0.019 0.115
## n.Tm:n.Grmn -0.003 -0.065 -0.051 -0.077 0.002 -0.063 0.181 0.046 0.187
## n.Tm:.G:.PO -0.032 0.176 -0.028 -0.052 -0.008 0.114 0.018 -0.007 0.114
## n.Tm:.G
## n.Time
## n.HL
## n.German
## c.PreviosSm
## c.PrevsOthr
## n.HL:n.Grmn
## n.Grmn:c.PO
## n.Tm:c.PrvO
## n.Tm:n.Grmn
## n.Tm:.G:.PO -0.033
# END --------------------------------------------------------------------------------------------------------------