library(readr)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
d <- read_csv("Desktop/Lab/Contextualizing Stigma and Trauma/LatineData_FINAL_Dataset_Scales.csv")
## New names:
## • `` -> `...1`
## Rows: 259 Columns: 48
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): GEN_8_TEXT, ETH_7_TEXT, BORN_1, AHELP
## dbl (43): ...1, AGE, GEN, EDU, EMP, INS_1, INS_2, ETH, INC, BORN, BORN_2, PR...
## lgl (1): EDU_11_TEXT
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
#data set with only variables of interest
# Select and rename columns in one step
d <- d %>%
select(
familism = PHFS_AVG,
help_seeking_attitudes = MHSAS_AVG,
self_stigma = SSOSH_AVG,
public_stigma = SSRPH_AVG,
act_help = AHELP,
prev_help = PRE_HELP
)
d$prev_help_new <- as.numeric(d$prev_help == 1) # This will make 1=TRUE (1; has sought help) and 2=FALSE (0; has not sought help)
# Verify the recoding worked
table(d$prev_help, d$prev_help_new, useNA = "ifany")
##
## 0 1 <NA>
## 1 0 175 0
## 2 83 0 0
## <NA> 0 0 1
# Then in your models, replace prev_help with prev_help_new
#loading packages
library(lavaan)
## This is lavaan 0.6-16
## lavaan is FREE software! Please report any bugs.
library(semPlot)
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(psych)
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
##
## The following object is masked from 'package:lavaan':
##
## cor2cov
library(jtools)
library(interactions)
library(ggplot2)
library(tidySEM)
## Loading required package: OpenMx
## OpenMx may run faster if it is compiled to take advantage of multiple cores.
##
## Attaching package: 'OpenMx'
##
## The following object is masked from 'package:psych':
##
## tr
##
## Registered S3 method overwritten by 'tidySEM':
## method from
## predict.MxModel OpenMx
##
## Attaching package: 'tidySEM'
##
## The following object is masked from 'package:jtools':
##
## get_data
Working the Moderated Mediation
Piecewise assemly of the moderated mediation
# Analysis 1: A simple moderation with prev_help_new as a covariate
Mod_a_path <- lm(self_stigma ~ public_stigma * familism + prev_help_new, data = d)
jtools::summ(Mod_a_path, digits = 3)
|
Observations
|
258 (1 missing obs. deleted)
|
|
Dependent variable
|
self_stigma
|
|
Type
|
OLS linear regression
|
|
F(4,253)
|
42.398
|
|
R²
|
0.401
|
|
Adj. R²
|
0.392
|
|
|
Est.
|
S.E.
|
t val.
|
p
|
|
(Intercept)
|
0.139
|
0.536
|
0.259
|
0.796
|
|
public_stigma
|
1.277
|
0.220
|
5.812
|
0.000
|
|
familism
|
0.259
|
0.137
|
1.892
|
0.060
|
|
prev_help_new
|
-0.438
|
0.087
|
-5.046
|
0.000
|
|
public_stigma:familism
|
-0.162
|
0.057
|
-2.833
|
0.005
|
|
Standard errors: OLS
|
# Graph interaction
interactions::interact_plot(Mod_a_path, pred = public_stigma, modx = familism) +
ylim(1, 10)
# Probing the interaction with simple slopes
interactions::sim_slopes(Mod_a_path, pred = public_stigma, modx = familism)
## JOHNSON-NEYMAN INTERVAL
##
## When familism is OUTSIDE the interval [6.06, 17.53], the slope of
## public_stigma is p < .05.
##
## Note: The range of observed values of familism is [1.00, 5.00]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of public_stigma when familism = 2.689588 (- 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.84 0.08 10.04 0.00
##
## Slope of public_stigma when familism = 3.676744 (Mean):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.68 0.06 11.10 0.00
##
## Slope of public_stigma when familism = 4.663900 (+ 1 SD):
##
## Est. S.E. t val. p
## ------ ------ -------- ------
## 0.52 0.08 6.28 0.00
# Analysis 2: Another simple moderation with prev_help_new as a covariate
Mod_b_path <- lm(help_seeking_attitudes ~ public_stigma * familism + prev_help_new, data = d)
jtools::summ(Mod_b_path, digits = 3)
|
Observations
|
257 (2 missing obs. deleted)
|
|
Dependent variable
|
help_seeking_attitudes
|
|
Type
|
OLS linear regression
|
|
F(4,252)
|
18.932
|
|
R²
|
0.231
|
|
Adj. R²
|
0.219
|
|
|
Est.
|
S.E.
|
t val.
|
p
|
|
(Intercept)
|
6.438
|
0.860
|
7.482
|
0.000
|
|
public_stigma
|
-0.898
|
0.352
|
-2.551
|
0.011
|
|
familism
|
0.066
|
0.219
|
0.301
|
0.764
|
|
prev_help_new
|
0.516
|
0.138
|
3.754
|
0.000
|
|
public_stigma:familism
|
0.062
|
0.091
|
0.680
|
0.497
|
|
Standard errors: OLS
|
# Graph interaction
interactions::interact_plot(Mod_b_path, pred = public_stigma, modx = familism) +
ylim(1, 10)
# Probing the interaction with simple slopes
interactions::sim_slopes(Mod_b_path, pred = public_stigma, modx = familism)
## JOHNSON-NEYMAN INTERVAL
##
## When familism is INSIDE the interval [-1.81, 6.31], the slope of
## public_stigma is p < .05.
##
## Note: The range of observed values of familism is [1.00, 5.00]
##
## SIMPLE SLOPES ANALYSIS
##
## Slope of public_stigma when familism = 2.694153 (- 1 SD):
##
## Est. S.E. t val. p
## ------- ------ -------- ------
## -0.73 0.13 -5.44 0.00
##
## Slope of public_stigma when familism = 3.680934 (Mean):
##
## Est. S.E. t val. p
## ------- ------ -------- ------
## -0.67 0.10 -6.85 0.00
##
## Slope of public_stigma when familism = 4.667715 (+ 1 SD):
##
## Est. S.E. t val. p
## ------- ------ -------- ------
## -0.61 0.13 -4.63 0.00
# Analysis 3: A simple mediation including prev_help_new as a covariate
LMedModel <- "
help_seeking_attitudes ~ b*self_stigma + c_p*public_stigma + c_prev_h*prev_help_new
self_stigma ~ a*public_stigma + c_prev_s*prev_help_new
# Intercepts
self_stigma ~ self_stigma.mean*1
help_seeking_attitudes ~ help_seeking_attitudes.mean*1
indirect := a*b
direct := c_p
total_c := c_p + (a*b)
"
set.seed(230925) # Required for reproducible results because lavaan introduces randomness into the calculations
LMed_fit <- lavaan::sem(LMedModel, data = d, se = "bootstrap", missing = "fiml")
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: 1 cases were deleted due to missing values in
## exogenous variable(s), while fixed.x = TRUE.
LMed_Sum <- lavaan::summary(LMed_fit, standardized = T, rsq = T, ci = TRUE)
LMed_ParEsts <- lavaan::parameterEstimates(LMed_fit, boot.ci.type = "bca.simple", standardized = TRUE)
LMed_Sum
## lavaan 0.6.16 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
##
## Used Total
## Number of observations 258 259
## Number of missing patterns 2
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## help_seeking_attitudes ~
## slf_ (b) -0.608 0.109 -5.558 0.000 -0.837
## pbl_ (c_p) -0.281 0.128 -2.200 0.028 -0.523
## pr__ (c_prv_h) 0.228 0.138 1.658 0.097 -0.042
## self_stigma ~
## pbl_ (a) 0.699 0.070 10.003 0.000 0.556
## pr__ (c_prv_s) -0.415 0.095 -4.392 0.000 -0.587
## ci.upper Std.lv Std.all
##
## -0.389 -0.608 -0.435
## -0.016 -0.281 -0.161
## 0.515 0.228 0.092
##
## 0.838 0.699 0.558
## -0.232 -0.415 -0.233
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .slf_stg (sl_.) 1.047 0.158 6.628 0.000 0.732 1.355
## .hlp_sk_ (h__.) 7.413 0.260 28.565 0.000 6.882 7.912
## Std.lv Std.all
## 1.047 1.259
## 7.413 6.386
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .hlp_skng_tttds 0.916 0.126 7.288 0.000 0.667 1.168
## .self_stigma 0.438 0.038 11.404 0.000 0.357 0.510
## Std.lv Std.all
## 0.916 0.680
## 0.438 0.634
##
## R-Square:
## Estimate
## hlp_skng_tttds 0.320
## self_stigma 0.366
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect -0.425 0.091 -4.680 0.000 -0.627 -0.261
## direct -0.281 0.128 -2.199 0.028 -0.523 -0.016
## total_c -0.706 0.101 -6.975 0.000 -0.884 -0.492
## Std.lv Std.all
## -0.425 -0.243
## -0.281 -0.161
## -0.706 -0.404
LMed_ParEsts
## lhs op rhs label
## 1 help_seeking_attitudes ~ self_stigma b
## 2 help_seeking_attitudes ~ public_stigma c_p
## 3 help_seeking_attitudes ~ prev_help_new c_prev_h
## 4 self_stigma ~ public_stigma a
## 5 self_stigma ~ prev_help_new c_prev_s
## 6 self_stigma ~1 self_stigma.mean
## 7 help_seeking_attitudes ~1 help_seeking_attitudes.mean
## 8 help_seeking_attitudes ~~ help_seeking_attitudes
## 9 self_stigma ~~ self_stigma
## 10 public_stigma ~~ public_stigma
## 11 public_stigma ~~ prev_help_new
## 12 prev_help_new ~~ prev_help_new
## 13 public_stigma ~1
## 14 prev_help_new ~1
## 15 indirect := a*b indirect
## 16 direct := c_p direct
## 17 total_c := c_p+(a*b) total_c
## est se z pvalue ci.lower ci.upper std.lv std.all std.nox
## 1 -0.608 0.109 -5.558 0.000 -0.798 -0.357 -0.608 -0.435 -0.435
## 2 -0.281 0.128 -2.200 0.028 -0.566 -0.054 -0.281 -0.161 -0.242
## 3 0.228 0.138 1.658 0.097 -0.032 0.529 0.228 0.092 0.197
## 4 0.699 0.070 10.003 0.000 0.557 0.838 0.699 0.558 0.841
## 5 -0.415 0.095 -4.392 0.000 -0.587 -0.232 -0.415 -0.233 -0.500
## 6 1.047 0.158 6.628 0.000 0.736 1.360 1.047 1.259 1.259
## 7 7.413 0.260 28.565 0.000 6.844 7.878 7.413 6.386 6.386
## 8 0.916 0.126 7.288 0.000 0.711 1.212 0.916 0.680 0.680
## 9 0.438 0.038 11.404 0.000 0.367 0.516 0.438 0.634 0.634
## 10 0.441 0.000 NA NA 0.441 0.441 0.441 1.000 0.441
## 11 0.001 0.000 NA NA 0.001 0.001 0.001 0.002 0.001
## 12 0.218 0.000 NA NA 0.218 0.218 0.218 1.000 0.218
## 13 2.216 0.000 NA NA 2.216 2.216 2.216 3.338 2.216
## 14 0.678 0.000 NA NA 0.678 0.678 0.678 1.452 0.678
## 15 -0.425 0.091 -4.680 0.000 -0.601 -0.245 -0.425 -0.243 -0.366
## 16 -0.281 0.128 -2.199 0.028 -0.566 -0.054 -0.281 -0.161 -0.242
## 17 -0.706 0.101 -6.975 0.000 -0.894 -0.504 -0.706 -0.404 -0.608
# Analysis 4: The moderated mediation - a combined analysis including prev_help_new
Combined <- '
# Equations
self_stigma ~ a1*public_stigma + a2*familism + a3*public_stigma:familism + c_prev_s*prev_help_new
help_seeking_attitudes ~ c_p1*public_stigma + c_p2*familism + c_p3*public_stigma:familism + b*self_stigma + c_prev_h*prev_help_new
# Intercepts
self_stigma ~ self_stigma.mean*1
help_seeking_attitudes ~ help_seeking_attitudes.mean*1
# Means, variances of W for simple slopes
familism ~ familism.mean*1
familism ~~ familism.var*familism
# Index of moderated mediation
imm := a3*b
indirect.SDbelow := a1*b + imm*(familism.mean - sqrt(familism.var))
indirect.mean := a1*b + imm*(familism.mean)
indirect.SDabove := a1*b + imm*(familism.mean + sqrt(familism.var))
direct.SDbelow := c_p1 + c_p3*(familism.mean - sqrt(familism.var))
direct.Smean := c_p1 + c_p3*(familism.mean)
direct.SDabove := c_p1 + c_p3*(familism.mean + sqrt(familism.var))
'
set.seed(230925) # Required for reproducible results
Combined_fit <- lavaan::sem(Combined, data = d, se = "bootstrap", missing = 'fiml', bootstrap = 1000)
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: 1 cases were deleted due to missing values in
## exogenous variable(s), while fixed.x = TRUE.
## Warning in lav_partable_vnames(FLAT, "ov.x", warn = TRUE): lavaan WARNING:
## model syntax contains variance/covariance/intercept formulas
## involving (an) exogenous variable(s): [familism]; These variables
## will now be treated as random introducing additional free
## parameters. If you wish to treat those variables as fixed, remove
## these formulas from the model syntax. Otherwise, consider adding
## the fixed.x = FALSE option.
cFITsum <- lavaan::summary(Combined_fit, standardized = TRUE, rsq = T, ci = TRUE)
cParamEsts <- lavaan::parameterEstimates(Combined_fit, boot.ci.type = "bca.simple", standardized = TRUE)
cFITsum
## lavaan 0.6.16 ended normally after 21 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Used Total
## Number of observations 258 259
## Number of missing patterns 2
##
## Model Test User Model:
##
## Test statistic 620.749
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## self_stigma ~
## pbl_ (a1) 1.277 0.221 5.768 0.000 0.895
## fmls (a2) 0.259 0.130 1.988 0.047 0.008
## pb_: (a3) -0.162 0.062 -2.620 0.009 -0.293
## pr__ (c_prv_s) -0.438 0.095 -4.606 0.000 -0.619
## help_seeking_attitudes ~
## pbl_ (c_p1) -0.142 0.424 -0.335 0.738 -0.846
## fmls (c_p2) 0.225 0.228 0.987 0.324 -0.168
## pb_: (c_p3) -0.035 0.106 -0.332 0.740 -0.284
## slf_ (b) -0.580 0.109 -5.341 0.000 -0.809
## pr__ (c_prv_h) 0.260 0.141 1.852 0.064 -0.025
## ci.upper Std.lv Std.all
##
## 1.737 1.277 0.896
## 0.545 0.259 0.269
## -0.054 -0.162 -0.547
## -0.243 -0.438 -0.216
##
## 0.851 -0.142 -0.082
## 0.748 0.225 0.193
## 0.141 -0.035 -0.098
## -0.369 -0.580 -0.478
## 0.542 0.260 0.106
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .slf_stg (sl_.) 0.139 0.486 0.285 0.775 -0.893 1.086
## .hlp_sk_ (h__.) 6.478 0.913 7.095 0.000 4.317 7.987
## familsm (fml.) 3.677 0.061 60.768 0.000 3.557 3.796
## Std.lv Std.all
## 0.139 0.147
## 6.478 5.634
## 3.677 3.732
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## familsm (fml.) 0.971 0.087 11.180 0.000 0.796 1.147
## .slf_stg 0.414 0.037 11.054 0.000 0.329 0.479
## .hlp_sk_ 0.896 0.125 7.187 0.000 0.644 1.135
## Std.lv Std.all
## 0.971 1.000
## 0.414 0.462
## 0.896 0.678
##
## R-Square:
## Estimate
## self_stigma 0.538
## hlp_skng_tttds 0.322
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## imm 0.094 0.039 2.397 0.017 0.031 0.187
## indirect.SDblw -0.488 0.101 -4.826 0.000 -0.714 -0.303
## indirect.mean -0.395 0.087 -4.562 0.000 -0.592 -0.243
## indirect.SDabv -0.302 0.088 -3.432 0.001 -0.503 -0.154
## direct.SDbelow -0.237 0.172 -1.377 0.169 -0.518 0.153
## direct.Smean -0.272 0.128 -2.129 0.033 -0.514 -0.001
## direct.SDabove -0.307 0.156 -1.967 0.049 -0.634 -0.004
## Std.lv Std.all
## 0.094 0.261
## -0.488 0.286
## -0.395 0.548
## -0.302 0.809
## -0.237 -0.350
## -0.272 -0.448
## -0.307 -0.546
cParamEsts
## lhs op rhs
## 1 self_stigma ~ public_stigma
## 2 self_stigma ~ familism
## 3 self_stigma ~ public_stigma:familism
## 4 self_stigma ~ prev_help_new
## 5 help_seeking_attitudes ~ public_stigma
## 6 help_seeking_attitudes ~ familism
## 7 help_seeking_attitudes ~ public_stigma:familism
## 8 help_seeking_attitudes ~ self_stigma
## 9 help_seeking_attitudes ~ prev_help_new
## 10 self_stigma ~1
## 11 help_seeking_attitudes ~1
## 12 familism ~1
## 13 familism ~~ familism
## 14 self_stigma ~~ self_stigma
## 15 help_seeking_attitudes ~~ help_seeking_attitudes
## 16 public_stigma ~~ public_stigma
## 17 public_stigma ~~ public_stigma:familism
## 18 public_stigma ~~ prev_help_new
## 19 public_stigma:familism ~~ public_stigma:familism
## 20 public_stigma:familism ~~ prev_help_new
## 21 prev_help_new ~~ prev_help_new
## 22 public_stigma ~1
## 23 public_stigma:familism ~1
## 24 prev_help_new ~1
## 25 imm := a3*b
## 26 indirect.SDbelow := a1*b+imm*(familism.mean-sqrt(familism.var))
## 27 indirect.mean := a1*b+imm*(familism.mean)
## 28 indirect.SDabove := a1*b+imm*(familism.mean+sqrt(familism.var))
## 29 direct.SDbelow := c_p1+c_p3*(familism.mean-sqrt(familism.var))
## 30 direct.Smean := c_p1+c_p3*(familism.mean)
## 31 direct.SDabove := c_p1+c_p3*(familism.mean+sqrt(familism.var))
## label est se z pvalue ci.lower ci.upper
## 1 a1 1.277 0.221 5.768 0.000 0.877 1.735
## 2 a2 0.259 0.130 1.988 0.047 0.001 0.540
## 3 a3 -0.162 0.062 -2.620 0.009 -0.292 -0.050
## 4 c_prev_s -0.438 0.095 -4.606 0.000 -0.616 -0.238
## 5 c_p1 -0.142 0.424 -0.335 0.738 -0.855 0.840
## 6 c_p2 0.225 0.228 0.987 0.324 -0.166 0.754
## 7 c_p3 -0.035 0.106 -0.332 0.740 -0.285 0.138
## 8 b -0.580 0.109 -5.341 0.000 -0.779 -0.342
## 9 c_prev_h 0.260 0.141 1.852 0.064 -0.008 0.560
## 10 self_stigma.mean 0.139 0.486 0.285 0.775 -0.867 1.114
## 11 help_seeking_attitudes.mean 6.478 0.913 7.095 0.000 4.274 7.964
## 12 familism.mean 3.677 0.061 60.768 0.000 3.566 3.801
## 13 familism.var 0.971 0.087 11.180 0.000 0.810 1.160
## 14 0.414 0.037 11.054 0.000 0.350 0.499
## 15 0.896 0.125 7.187 0.000 0.704 1.222
## 16 0.441 0.000 NA NA 0.441 0.441
## 17 1.447 0.000 NA NA 1.447 1.447
## 18 0.001 0.000 NA NA 0.001 0.001
## 19 10.211 0.000 NA NA 10.211 10.211
## 20 -0.084 0.000 NA NA -0.084 -0.084
## 21 0.218 0.000 NA NA 0.218 0.218
## 22 2.216 0.000 NA NA 2.216 2.216
## 23 8.070 0.000 NA NA 8.070 8.070
## 24 0.678 0.000 NA NA 0.678 0.678
## 25 imm 0.094 0.039 2.397 0.017 0.029 0.182
## 26 indirect.SDbelow -0.488 0.101 -4.826 0.000 -0.684 -0.278
## 27 indirect.mean -0.395 0.087 -4.562 0.000 -0.570 -0.236
## 28 indirect.SDabove -0.302 0.088 -3.432 0.001 -0.508 -0.156
## 29 direct.SDbelow -0.237 0.172 -1.377 0.169 -0.542 0.128
## 30 direct.Smean -0.272 0.128 -2.129 0.033 -0.564 -0.048
## 31 direct.SDabove -0.307 0.156 -1.967 0.049 -0.675 -0.039
## std.lv std.all std.nox
## 1 1.277 0.896 1.349
## 2 0.259 0.269 0.181
## 3 -0.162 -0.547 -0.171
## 4 -0.438 -0.216 -0.463
## 5 -0.142 -0.082 -0.124
## 6 0.225 0.193 0.130
## 7 -0.035 -0.098 -0.031
## 8 -0.580 -0.478 -0.478
## 9 0.260 0.106 0.226
## 10 0.139 0.147 0.147
## 11 6.478 5.634 5.634
## 12 3.677 3.732 3.732
## 13 0.971 1.000 1.000
## 14 0.414 0.462 0.462
## 15 0.896 0.678 0.678
## 16 0.441 1.000 0.441
## 17 1.447 0.682 1.447
## 18 0.001 0.002 0.001
## 19 10.211 1.000 10.211
## 20 -0.084 -0.057 -0.084
## 21 0.218 1.000 0.218
## 22 2.216 3.338 2.216
## 23 8.070 2.526 8.070
## 24 0.678 1.452 0.678
## 25 0.094 0.261 0.082
## 26 -0.488 0.286 -0.421
## 27 -0.395 0.548 -0.339
## 28 -0.302 0.809 -0.257
## 29 -0.237 -0.350 -0.207
## 30 -0.272 -0.448 -0.238
## 31 -0.307 -0.546 -0.269