setwd("C:/Work Files/Teaching/PSY 8190/Data Assignments/Data Assignment 2")Data Assignment 2 Answer Key 2025
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(knitr)
library(ggplot2)
library(lme4)Loading required package: Matrix
Attaching package: 'Matrix'
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steplibrary(lavaan)This is lavaan 0.6-19
lavaan is FREE software! Please report any bugs.library(psych)
Attaching package: 'psych'
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cor2cov
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VIM is ready to use.
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Attaching package: 'VIM'
The following object is masked from 'package:datasets':
sleepAssn_2_Data <-read.csv("job_performance_long.csv")
Assn_2_Data_Wide <-read.csv("job_performance_wide.csv")head(Assn_2_Data,15) id wave performance_continuous gender qualifications
1 1 1 1.408250 1 3
2 1 2 2.129363 1 3
3 1 3 2.797420 1 3
4 1 4 2.453070 1 3
5 1 5 2.529704 1 3
6 1 6 2.338785 1 3
7 2 1 2.038001 0 5
8 2 2 1.564303 0 5
9 2 3 1.888694 0 5
10 2 4 2.870881 0 5
11 2 5 3.141473 0 5
12 2 6 2.595409 0 5
13 3 1 2.921425 0 4
14 3 2 3.760158 0 4
15 3 3 3.958660 0 4names(Assn_2_Data)[1] "id" "wave" "performance_continuous"
[4] "gender" "qualifications" str(Assn_2_Data)'data.frame': 3600 obs. of 5 variables:
$ id : int 1 1 1 1 1 1 2 2 2 2 ...
$ wave : int 1 2 3 4 5 6 1 2 3 4 ...
$ performance_continuous: num 1.41 2.13 2.8 2.45 2.53 ...
$ gender : int 1 1 1 1 1 1 0 0 0 0 ...
$ qualifications : int 3 3 3 3 3 3 5 5 5 5 ...Assn_2_Data$gender <- factor(Assn_2_Data$gender,
levels = c(0,1),
labels = c("Female","Male"))
Assn_2_Data$qualifications <- factor(Assn_2_Data$qualifications,
levels = c(1,2,3,4,5),
labels = c("None","Unsuitable","Suitable","Aligned","Exceptional"),ordered = TRUE)
str(Assn_2_Data$gender) Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 1 1 1 1 ...str(Assn_2_Data$qualifications) Ord.factor w/ 5 levels "None"<"Unsuitable"<..: 3 3 3 3 3 3 5 5 5 5 ...table(Assn_2_Data$gender)
Female Male
1830 1770 table(Assn_2_Data$qualifications)
None Unsuitable Suitable Aligned Exceptional
438 744 1038 972 408 mean_data <- Assn_2_Data %>%
group_by(wave) %>%
summarise(mean_performance = mean(performance_continuous),
se_performance = sd(performance_continuous) / sqrt(n()))
mean_traj_plot <-ggplot(mean_data, aes(x = wave, y = mean_performance)) +
geom_line(color = "blue", linewidth = 1) +
geom_point(color = "blue", size = 2) +
geom_errorbar(aes(ymin = mean_performance - se_performance, ymax = mean_performance + se_performance), width = 0.2) +
labs(title = "Mean Trajectory Over Time",
x = "Wave",
y = "Performance") +
theme_minimal()mean_traj_plot
mean_traj_plot +
ylim(0,6) 
hist(Assn_2_Data$performance_continuous)
ggplot(Assn_2_Data, aes(x = wave, y = performance_continuous, group = id, color = gender)) +
geom_line(alpha = 0.5) +
geom_point(alpha = 0.5) +
labs(title = "Individual Trajectories (Spaghetti Plot)",
x = "Wave",
y = "Performance") +
theme_minimal()
describe(Assn_2_Data[,-1]) vars n mean sd median trimmed mad min max range
wave 1 3600 3.50 1.71 3.50 3.50 2.22 1.00 6.00 5.00
performance_continuous 2 3600 2.68 1.00 2.66 2.67 0.97 -0.68 7.11 7.79
gender* 3 3600 1.49 0.50 1.00 1.49 0.00 1.00 2.00 1.00
qualifications* 4 3600 3.05 1.19 3.00 3.06 1.48 1.00 5.00 4.00
skew kurtosis se
wave 0.00 -1.27 0.03
performance_continuous 0.16 0.18 0.02
gender* 0.03 -2.00 0.01
qualifications* -0.12 -0.87 0.02aggr_plot <- aggr(Assn_2_Data[,-1], col=c('navyblue','red'), numbers=TRUE, sortVars=TRUE, labels=names(Assn_2_Data[,-1]), cex.axis=.7, gap=3, ylab=c("Histogram of missing data","Pattern"))
Variables sorted by number of missings:
Variable Count
wave 0
performance_continuous 0
gender 0
qualifications 0UC_model <- lmer(performance_continuous ~ wave +
(1 + wave | id), data = Assn_2_Data)
# Summary of the model
summary(UC_model)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: performance_continuous ~ wave + (1 + wave | id)
Data: Assn_2_Data
REML criterion at convergence: 6892.5
Scaled residuals:
Min 1Q Median 3Q Max
-2.9065 -0.5784 -0.0302 0.5874 3.6305
Random effects:
Groups Name Variance Std.Dev. Corr
id (Intercept) 0.44856 0.6697
wave 0.02071 0.1439 -0.06
Residual 0.21140 0.4598
Number of obs: 3600, groups: id, 600
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 2.159e+00 3.245e-02 5.990e+02 66.53 <2e-16 ***
wave 1.485e-01 7.393e-03 5.990e+02 20.09 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
wave -0.336Cond_model <- lmer(performance_continuous ~ wave + gender + qualifications + wave:qualifications + wave:gender + wave:gender:qualifications
+ (1 + wave | id), data = Assn_2_Data)
# Summary of the model
summary(Cond_model)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula:
performance_continuous ~ wave + gender + qualifications + wave:qualifications +
wave:gender + wave:gender:qualifications + (1 + wave | id)
Data: Assn_2_Data
REML criterion at convergence: 6734.1
Scaled residuals:
Min 1Q Median 3Q Max
-2.8147 -0.5851 -0.0408 0.5912 3.6394
Random effects:
Groups Name Variance Std.Dev. Corr
id (Intercept) 0.4195 0.6477
wave 0.0132 0.1149 -0.09
Residual 0.2114 0.4598
Number of obs: 3600, groups: id, 600
Fixed effects:
Estimate Std. Error df t value
(Intercept) 2.324942 0.045998 593.987662 50.544
wave 0.182212 0.009656 599.338049 18.871
genderMale -0.324492 0.063457 593.987797 -5.114
qualifications.L -0.201932 0.087807 593.987743 -2.300
qualifications.Q 0.021205 0.080657 593.987907 0.263
qualifications.C 0.017503 0.071741 593.987813 0.244
qualifications^4 0.078756 0.063235 593.987880 1.245
wave:qualifications.L 0.233208 0.023748 640.175652 9.820
wave:qualifications.Q -0.013509 0.021949 640.387962 -0.615
wave:qualifications.C -0.037472 0.019600 640.510573 -1.912
wave:qualifications^4 0.016680 0.017552 640.911320 0.950
wave:genderMale -0.081882 0.013866 611.327578 -5.905
wave:genderMale:qualifications.L -0.093329 0.033070 590.003337 -2.822
wave:genderMale:qualifications.Q -0.010108 0.030358 590.003337 -0.333
wave:genderMale:qualifications.C 0.041412 0.026970 590.003337 1.535
wave:genderMale:qualifications^4 -0.017794 0.023754 590.003336 -0.749
Pr(>|t|)
(Intercept) < 2e-16 ***
wave < 2e-16 ***
genderMale 4.27e-07 ***
qualifications.L 0.02181 *
qualifications.Q 0.79271
qualifications.C 0.80734
qualifications^4 0.21346
wave:qualifications.L < 2e-16 ***
wave:qualifications.Q 0.53847
wave:qualifications.C 0.05633 .
wave:qualifications^4 0.34232
wave:genderMale 5.85e-09 ***
wave:genderMale:qualifications.L 0.00493 **
wave:genderMale:qualifications.Q 0.73928
wave:genderMale:qualifications.C 0.12520
wave:genderMale:qualifications^4 0.45408
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 16 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need itnames(Assn_2_Data_Wide)[1] "id" "gender" "qualifications"
[4] "performance_wave_1" "performance_wave_2" "performance_wave_3"
[7] "performance_wave_4" "performance_wave_5" "performance_wave_6"UC_LGC <-'
I=~ 1*performance_wave_1 + 1*performance_wave_2 + 1*performance_wave_3 + 1*performance_wave_4 + 1*performance_wave_5 + 1*performance_wave_6
S=~ 0*performance_wave_1 + 1*performance_wave_2 + 2*performance_wave_3 + 3*performance_wave_4 + 4*performance_wave_5 + 5*performance_wave_6
'
UC_LGC_fit <- growth(UC_LGC, estimator= "ML", data=Assn_2_Data_Wide, mimic = "Mplus", missing = "FIML")
summary(UC_LGC_fit, fit.measures = TRUE, standardized=TRUE)lavaan 0.6-19 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 11
Number of observations 600
Number of missing patterns 1
Model Test User Model:
Test statistic 14.396
Degrees of freedom 16
P-value (Chi-square) 0.569
Model Test Baseline Model:
Test statistic 2361.066
Degrees of freedom 15
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.001
Robust Comparative Fit Index (CFI) 1.000
Robust Tucker-Lewis Index (TLI) 1.001
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -3800.564
Loglikelihood unrestricted model (H1) -3793.366
Akaike (AIC) 7623.128
Bayesian (BIC) 7671.495
Sample-size adjusted Bayesian (SABIC) 7636.573
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.034
P-value H_0: RMSEA <= 0.050 0.998
P-value H_0: RMSEA >= 0.080 0.000
Robust RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.034
P-value H_0: Robust RMSEA <= 0.050 0.998
P-value H_0: Robust RMSEA >= 0.080 0.000
Standardized Root Mean Square Residual:
SRMR 0.016
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
I =~
performnc_wv_1 1.000 0.659 0.774
performnc_wv_2 1.000 0.659 0.757
performnc_wv_3 1.000 0.659 0.726
performnc_wv_4 1.000 0.659 0.667
performnc_wv_5 1.000 0.659 0.625
performnc_wv_6 1.000 0.659 0.579
S =~
performnc_wv_1 0.000 0.000 0.000
performnc_wv_2 1.000 0.143 0.164
performnc_wv_3 2.000 0.285 0.314
performnc_wv_4 3.000 0.428 0.433
performnc_wv_5 4.000 0.571 0.541
performnc_wv_6 5.000 0.713 0.626
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
I ~~
S 0.010 0.006 1.542 0.123 0.106 0.106
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
I 2.327 0.031 74.598 0.000 3.530 3.530
S 0.149 0.008 19.221 0.000 1.044 1.044
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.performnc_wv_1 0.291 0.025 11.560 0.000 0.291 0.401
.performnc_wv_2 0.284 0.020 13.911 0.000 0.284 0.374
.performnc_wv_3 0.268 0.018 14.528 0.000 0.268 0.326
.performnc_wv_4 0.299 0.021 14.566 0.000 0.299 0.306
.performnc_wv_5 0.274 0.021 12.999 0.000 0.274 0.246
.performnc_wv_6 0.253 0.025 9.972 0.000 0.253 0.195
I 0.435 0.034 12.600 0.000 1.000 1.000
S 0.020 0.002 9.033 0.000 1.000 1.000Cond_LGC <-'
I=~ 1*performance_wave_1 + 1*performance_wave_2 + 1*performance_wave_3 + 1*performance_wave_4 + 1*performance_wave_5 + 1*performance_wave_6
S=~ 0*performance_wave_1 + 1*performance_wave_2 + 2*performance_wave_3 + 3*performance_wave_4 + 4*performance_wave_5 + 5*performance_wave_6
I ~ gender + qualifications
S ~ gender + qualifications
'
Cond_LGC_fit <- growth(Cond_LGC, estimator= "ML", data=Assn_2_Data_Wide, mimic = "Mplus", missing = "FIML")
summary(Cond_LGC_fit, fit.measures = TRUE, standardized=TRUE)lavaan 0.6-19 ended normally after 38 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 15
Number of observations 600
Number of missing patterns 1
Model Test User Model:
Test statistic 25.287
Degrees of freedom 24
P-value (Chi-square) 0.390
Model Test Baseline Model:
Test statistic 2572.279
Degrees of freedom 27
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.999
Tucker-Lewis Index (TLI) 0.999
Robust Comparative Fit Index (CFI) 0.999
Robust Tucker-Lewis Index (TLI) 0.999
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -3700.403
Loglikelihood unrestricted model (H1) -3687.760
Akaike (AIC) 7430.806
Bayesian (BIC) 7496.760
Sample-size adjusted Bayesian (SABIC) 7449.139
Root Mean Square Error of Approximation:
RMSEA 0.009
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.035
P-value H_0: RMSEA <= 0.050 0.999
P-value H_0: RMSEA >= 0.080 0.000
Robust RMSEA 0.009
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.035
P-value H_0: Robust RMSEA <= 0.050 0.999
P-value H_0: Robust RMSEA >= 0.080 0.000
Standardized Root Mean Square Residual:
SRMR 0.016
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
I =~
performnc_wv_1 1.000 0.659 0.771
performnc_wv_2 1.000 0.659 0.759
performnc_wv_3 1.000 0.659 0.725
performnc_wv_4 1.000 0.659 0.667
performnc_wv_5 1.000 0.659 0.627
performnc_wv_6 1.000 0.659 0.577
S =~
performnc_wv_1 0.000 0.000 0.000
performnc_wv_2 1.000 0.142 0.163
performnc_wv_3 2.000 0.283 0.311
performnc_wv_4 3.000 0.425 0.430
performnc_wv_5 4.000 0.566 0.539
performnc_wv_6 5.000 0.708 0.619
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
I ~
gender -0.394 0.060 -6.544 0.000 -0.599 -0.299
qualifications -0.002 0.025 -0.096 0.923 -0.004 -0.004
S ~
gender -0.081 0.014 -5.782 0.000 -0.569 -0.284
qualifications 0.061 0.006 10.361 0.000 0.429 0.510
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.I ~~
.S 0.002 0.006 0.429 0.668 0.034 0.034
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.I 2.529 0.088 28.579 0.000 3.839 3.839
.S 0.004 0.020 0.179 0.858 0.026 0.026
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.performnc_wv_1 0.295 0.025 11.844 0.000 0.295 0.405
.performnc_wv_2 0.278 0.020 13.958 0.000 0.278 0.370
.performnc_wv_3 0.271 0.019 14.568 0.000 0.271 0.327
.performnc_wv_4 0.298 0.020 14.626 0.000 0.298 0.306
.performnc_wv_5 0.267 0.020 13.179 0.000 0.267 0.241
.performnc_wv_6 0.266 0.025 10.737 0.000 0.266 0.204
.I 0.395 0.032 12.238 0.000 0.910 0.910
.S 0.013 0.002 6.989 0.000 0.655 0.655