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Mplus VERSION 8.3
MUTHEN & MUTHEN
05/20/2021 11:01 AM
INPUT INSTRUCTIONS
TITLE:
Example Model;
DATA:
FILE = ecls_acad.dat;
VARIABLE:
NAMES = read1 math1 gk1 lrn_p1
read2 math2 gk2 lrn_p2;
MISSING = .;
USEVAR = read1 math1 gk1
read2 math2 gk2;
MODEL:
! Factor Loadings (Lambda)
eta_1 BY math1@1
read1
gk1;
eta_2 BY math2@1
read2
gk2;
! Factor Variances (Psi)
eta_1 eta_2;
! Latent Variable Regressions (Beta)
eta_2 ON eta_1*.8;
! Factor Means (alpha)
[eta_1@0 eta_2@0];
! Unique Variances & Covariances (Theta)
math1 read1 gk1 math2 read2 gk2;
math1 WITH math2;
read1 WITH read2;
gk1 WITH gk2;
! Measurement Intercepts (tau)
[math1 read1 gk1 math2 read2 gk2];
OUTPUT: SAMPSTAT STANDARDIZED TECH1;
INPUT READING TERMINATED NORMALLY
Example Model;
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20601
Number of dependent variables 6
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
READ1 MATH1 GK1 READ2 MATH2 GK2
Continuous latent variables
ETA_1 ETA_2
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Input data file(s)
ecls_acad.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 29
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
READ1 0.855
MATH1 0.854 0.905
GK1 0.852 0.852 0.853
READ2 0.813 0.828 0.811 0.919
MATH2 0.813 0.859 0.811 0.918 0.954
GK2 0.812 0.827 0.810 0.917 0.917
Covariance Coverage
GK2
________
GK2 0.918
SAMPLE STATISTICS
ESTIMATED SAMPLE STATISTICS
Means
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
34.779 25.822 21.758 45.958 36.131
Means
GK2
________
26.807
Covariances
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
READ1 103.977
MATH1 66.918 82.464
GK1 39.491 42.933 57.779
READ2 119.385 86.454 49.686 198.551
MATH2 79.019 90.512 54.606 116.313 144.225
GK2 39.870 43.417 51.801 54.418 59.383
Covariances
GK2
________
GK2 62.350
Correlations
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
READ1 1.000
MATH1 0.723 1.000
GK1 0.510 0.622 1.000
READ2 0.831 0.676 0.464 1.000
MATH2 0.645 0.830 0.598 0.687 1.000
GK2 0.495 0.605 0.863 0.489 0.626
Correlations
GK2
________
GK2 1.000
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -367574.510
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
READ1 35.215 2.936 21.010 0.01% 27.390 31.840 33.460
17622.000 104.009 16.301 138.510 0.01% 35.210 40.830
MATH1 25.905 1.410 10.510 0.01% 18.560 22.430 24.440
18636.000 82.791 4.186 115.650 0.01% 26.400 32.130
GK1 22.231 0.257 6.985 0.03% 15.218 19.676 21.872
17564.000 56.382 -0.570 47.691 0.01% 24.072 28.938
READ2 46.459 2.268 22.230 0.01% 36.520 41.860 44.340
18937.000 196.977 8.841 156.850 0.03% 46.640 52.850
MATH2 36.273 1.058 11.570 0.01% 26.300 31.710 34.610
19649.000 144.100 2.351 113.800 0.01% 37.920 45.030
GK2 27.079 -0.066 7.274 0.01% 19.741 25.140 27.291
18903.000 62.186 -0.638 48.345 0.01% 29.491 34.237
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 22
Loglikelihood
H0 Value -367709.517
H1 Value -367574.510
Information Criteria
Akaike (AIC) 735463.035
Bayesian (BIC) 735637.563
Sample-Size Adjusted BIC 735567.648
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 270.014
Degrees of Freedom 5
P-Value 0.0000
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.051
90 Percent C.I. 0.046 0.056
Probability RMSEA <= .05 0.397
CFI/TLI
CFI 0.997
TLI 0.991
Chi-Square Test of Model Fit for the Baseline Model
Value 91489.282
Degrees of Freedom 15
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.010
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
ETA_1 BY
MATH1 1.000 0.000 999.000 999.000
READ1 0.892 0.009 102.554 0.000
GK1 0.575 0.006 89.703 0.000
ETA_2 BY
MATH2 1.000 0.000 999.000 999.000
READ2 0.951 0.009 101.979 0.000
GK2 0.470 0.005 90.199 0.000
ETA_2 ON
ETA_1 1.224 0.007 175.086 0.000
MATH1 WITH
MATH2 -0.570 0.645 -0.884 0.377
READ1 WITH
READ2 43.113 0.782 55.166 0.000
GK1 WITH
GK2 26.202 0.356 73.594 0.000
Means
ETA_1 0.000 0.000 999.000 999.000
Intercepts
READ1 34.791 0.073 475.674 0.000
MATH1 25.821 0.064 402.153 0.000
GK1 21.761 0.054 401.270 0.000
READ2 45.954 0.100 458.478 0.000
MATH2 36.131 0.084 428.596 0.000
GK2 26.811 0.056 480.977 0.000
ETA_2 0.000 0.000 999.000 999.000
Variances
ETA_1 74.575 0.994 75.048 0.000
Residual Variances
READ1 44.894 0.647 69.433 0.000
MATH1 7.887 0.558 14.122 0.000
GK1 32.447 0.389 83.515 0.000
READ2 88.564 1.198 73.928 0.000
MATH2 20.957 0.982 21.337 0.000
GK2 34.343 0.406 84.684 0.000
ETA_2 11.649 0.359 32.447 0.000
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
ETA_1 BY
MATH1 0.951 0.004 265.078 0.000
READ1 0.755 0.004 180.531 0.000
GK1 0.657 0.005 136.770 0.000
ETA_2 BY
MATH2 0.925 0.004 247.206 0.000
READ2 0.746 0.004 183.342 0.000
GK2 0.665 0.005 141.235 0.000
ETA_2 ON
ETA_1 0.952 0.001 641.371 0.000
MATH1 WITH
MATH2 -0.044 0.052 -0.846 0.398
READ1 WITH
READ2 0.684 0.005 134.659 0.000
GK1 WITH
GK2 0.785 0.003 239.758 0.000
Means
ETA_1 0.000 0.000 999.000 999.000
Intercepts
READ1 3.407 0.019 178.583 0.000
MATH1 2.843 0.016 177.473 0.000
GK1 2.880 0.017 172.620 0.000
READ2 3.249 0.018 179.622 0.000
MATH2 3.008 0.017 181.181 0.000
GK2 3.415 0.019 182.316 0.000
ETA_2 0.000 0.000 999.000 999.000
Variances
ETA_1 1.000 0.000 999.000 999.000
Residual Variances
READ1 0.431 0.006 68.255 0.000
MATH1 0.096 0.007 14.017 0.000
GK1 0.568 0.006 90.035 0.000
READ2 0.443 0.006 72.855 0.000
MATH2 0.145 0.007 21.003 0.000
GK2 0.557 0.006 88.919 0.000
ETA_2 0.094 0.003 33.448 0.000
STDY Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
ETA_1 BY
MATH1 0.951 0.004 265.078 0.000
READ1 0.755 0.004 180.531 0.000
GK1 0.657 0.005 136.770 0.000
ETA_2 BY
MATH2 0.925 0.004 247.206 0.000
READ2 0.746 0.004 183.342 0.000
GK2 0.665 0.005 141.235 0.000
ETA_2 ON
ETA_1 0.952 0.001 641.371 0.000
MATH1 WITH
MATH2 -0.044 0.052 -0.846 0.398
READ1 WITH
READ2 0.684 0.005 134.659 0.000
GK1 WITH
GK2 0.785 0.003 239.758 0.000
Means
ETA_1 0.000 0.000 999.000 999.000
Intercepts
READ1 3.407 0.019 178.583 0.000
MATH1 2.843 0.016 177.473 0.000
GK1 2.880 0.017 172.620 0.000
READ2 3.249 0.018 179.622 0.000
MATH2 3.008 0.017 181.181 0.000
GK2 3.415 0.019 182.316 0.000
ETA_2 0.000 0.000 999.000 999.000
Variances
ETA_1 1.000 0.000 999.000 999.000
Residual Variances
READ1 0.431 0.006 68.255 0.000
MATH1 0.096 0.007 14.017 0.000
GK1 0.568 0.006 90.035 0.000
READ2 0.443 0.006 72.855 0.000
MATH2 0.145 0.007 21.003 0.000
GK2 0.557 0.006 88.919 0.000
ETA_2 0.094 0.003 33.448 0.000
STD Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
ETA_1 BY
MATH1 8.636 0.058 150.097 0.000
READ1 7.705 0.068 112.922 0.000
GK1 4.964 0.052 96.175 0.000
ETA_2 BY
MATH2 11.105 0.077 143.630 0.000
READ2 10.556 0.093 113.955 0.000
GK2 5.223 0.053 98.489 0.000
ETA_2 ON
ETA_1 0.952 0.001 641.371 0.000
MATH1 WITH
MATH2 -0.570 0.645 -0.884 0.377
READ1 WITH
READ2 43.113 0.782 55.166 0.000
GK1 WITH
GK2 26.202 0.356 73.594 0.000
Means
ETA_1 0.000 0.000 999.000 999.000
Intercepts
READ1 34.791 0.073 475.674 0.000
MATH1 25.821 0.064 402.153 0.000
GK1 21.761 0.054 401.270 0.000
READ2 45.954 0.100 458.478 0.000
MATH2 36.131 0.084 428.596 0.000
GK2 26.811 0.056 480.977 0.000
ETA_2 0.000 0.000 999.000 999.000
Variances
ETA_1 1.000 0.000 999.000 999.000
Residual Variances
READ1 44.894 0.647 69.433 0.000
MATH1 7.887 0.558 14.122 0.000
GK1 32.447 0.389 83.515 0.000
READ2 88.564 1.198 73.928 0.000
MATH2 20.957 0.982 21.337 0.000
GK2 34.343 0.406 84.684 0.000
ETA_2 0.094 0.003 33.448 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
READ1 0.569 0.006 90.266 0.000
MATH1 0.904 0.007 132.539 0.000
GK1 0.432 0.006 68.385 0.000
READ2 0.557 0.006 91.671 0.000
MATH2 0.855 0.007 123.603 0.000
GK2 0.443 0.006 70.617 0.000
Latent Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
ETA_2 0.906 0.003 320.685 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.646E-05
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
1 2 3 4 5
NU
GK2
________
6
LAMBDA
ETA_1 ETA_2
________ ________
READ1 7 0
MATH1 0 0
GK1 8 0
READ2 0 9
MATH2 0 0
GK2 0 10
THETA
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
READ1 11
MATH1 0 12
GK1 0 0 13
READ2 14 0 0 15
MATH2 0 16 0 0 17
GK2 0 0 18 0 0
THETA
GK2
________
GK2 19
ALPHA
ETA_1 ETA_2
________ ________
0 0
BETA
ETA_1 ETA_2
________ ________
ETA_1 0 0
ETA_2 20 0
PSI
ETA_1 ETA_2
________ ________
ETA_1 21
ETA_2 0 22
STARTING VALUES
NU
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
35.215 25.905 22.231 46.459 36.273
NU
GK2
________
27.079
LAMBDA
ETA_1 ETA_2
________ ________
READ1 0.920 0.000
MATH1 1.000 0.000
GK1 0.590 0.000
READ2 0.000 0.916
MATH2 0.000 1.000
GK2 0.000 0.468
THETA
READ1 MATH1 GK1 READ2 MATH2
________ ________ ________ ________ ________
READ1 52.005
MATH1 0.000 41.395
GK1 0.000 0.000 28.191
READ2 0.000 0.000 0.000 98.488
MATH2 0.000 0.000 0.000 0.000 72.050
GK2 0.000 0.000 0.000 0.000 0.000
THETA
GK2
________
GK2 31.093
ALPHA
ETA_1 ETA_2
________ ________
0.000 0.000
BETA
ETA_1 ETA_2
________ ________
ETA_1 0.000 0.000
ETA_2 0.800 0.000
PSI
ETA_1 ETA_2
________ ________
ETA_1 0.050
ETA_2 0.000 0.050
DIAGRAM INFORMATION
Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
Diagram output
e:\kjgrimm\documents\ucd\organization\workshops\ati\apa-ati lsem 2021\finalfiles\a.reviewsemmplus.dgm
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Ending Time: 11:01:55
Elapsed Time: 00:00:01
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Intensive Longitudinal Data
Intraindividual Variability Metrics Computation
Overview
This tutorial illustrates calculation of intraindividual variability metrics. Specifically, this tutorial demonstrates calculation of a few univariate metrics, a few bivariate metrics, and a few multivariate metrics - as well as how these metrics are related to other individual differences.
Outline
A. Univariate IIV Metrics
- iCount, iMean, iSD, iSkew, iKurtosis, iEntropy
B. Bivariate IIV Metrics
- iCor, iCov, iReg
C. Multivariate IIV Metrics
- Determinant of a matrix, Frobenius Norm
D. Selected Readings
- Benson, L., Ram, N., Almeida, D. M., Zautra, A. J., & Ong, A. D. (2017). Fusing biodiversity metrics into investigations of daily life: Illustrations and recommendations with emodiversity. The Journals of Gerontology: Series B, 73(1), 75-86.
- Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009). Using derivative estimates to describe intraindividual variability at multiple time scales. Psychological methods, 14(4), 367.
- Jahng, S., Wood, P. K., & Trull, T. J. (2008). Analysis of affective instability in ecological momentary assessment: Indices using successive difference and group comparison via multilevel modeling. Psychological methods, 13(4), 354.
- Ram, N., Benson, L., Brick, T. R., Conroy, D. E., & Pincus, A. L. (2017). Behavioral landscapes and earth mover’s distance: A new approach for studying individual differences in density distributions. Journal of research in personality, 69, 191-205.
- Ram, N., & Gerstorf, D. (2009). Time-structured and net intraindividual variability: tools for examining the development of dynamic characteristics and processes. Psychology and aging, 24(4), 778.
Preliminaries
Loading Libraries
Loading libraries used in this script.
library(psych) # for describing the data
library(plyr) #for data manipulation
library(ggplot2) # for data visualization
library(entropy) #for entropy calculation
library(nFactors) #factor analysisLoading Data
Our example makes use of the person-level and interaction-level (EMA-type) AMIB data files. We make use of person-level personality variables and a small set of interaction-level variables.
Loading person-level file and subsetting to variables of interest
#set filepath for data file
filepath <- "https://quantdev.ssri.psu.edu/sites/qdev/files/AMIBshare_persons_2019_0501.csv"
#read in the .csv file using the url() function
AMIB_persons <- read.csv(file=url(filepath),header=TRUE)
#subsetting to variables of interest
AMIB_persons <- AMIB_persons[ ,c("id","bfi_o","bfi_c","bfi_e","bfi_a","bfi_n")]Loading day-level file (T = 21) and subsetting to variables of interest.
#set filepath for data file
filepath <- "https://quantdev.ssri.psu.edu/sites/qdev/files/AMIBshare_phase2_daily_2019_0501.csv"
#read in the .csv file using the url() function
AMIB_daily <- read.csv(file=url(filepath),header=TRUE)1. Univariate IIV Metrics
There are several types of univariate IIV metrics that differ based on the type of data (continuous, binary, count), and conceptual meanings. For example, the iMean, iSD, iSkew, and iKurtosis are the first four distribution moments, utilize continuous data, and are unstructured with respect to time. iMSSD and iPAC also utilize continuous data, but do acount for time dependencies in the data. iEntropy and iTurbulence pertain to categorical data.
We illustrate just a few. The general principle is to use the functions in the plyr package to split the data by “id” and summarize each person’s data using a specifci fucntion (e.g., mean, sd). We will use this same approach when preparing data in later analyses.
Calculating univariate IIV metrics.
istats_univariate <- ddply(AMIB_daily, "id", summarize,
icount_posaff = sum(!is.na(posaff)), #count of observations
imean_posaff = mean(posaff, na.rm=TRUE), #imean (continuous)
isd_posaff = sd(posaff, na.rm=TRUE), #isd (continuous)
iskew_posaff = skew(posaff, na.rm=TRUE), #iskew (continuous)
ikurt_posaff = kurtosi(posaff, na.rm=TRUE), # ikurtosis (continuous)
ientropy_stress= entropy(table(stress,
useNA="no"))) #(categorical)Look at univariate IIV metrics data
round(head(istats_univariate),2)## id icount_posaff imean_posaff isd_posaff iskew_posaff ikurt_posaff
## 1 203 22 4.42 0.84 -0.70 0.13
## 2 204 22 3.10 1.17 -0.58 -1.19
## 3 205 22 4.32 0.68 -0.73 -0.53
## 4 208 22 3.92 0.67 0.11 -0.86
## 5 211 22 2.81 0.85 0.70 -0.15
## 6 214 15 4.16 1.01 -0.46 -0.82
## ientropy_stress
## 1 1.00
## 2 1.49
## 3 1.67
## 4 1.02
## 5 1.36
## 6 1.90Describe the bivariate IIV metrics
describe(istats_univariate[-1])## vars n mean sd median trimmed mad min max range skew
## icount_posaff 1 30 20.90 2.58 22.00 21.58 0.00 14.00 22.00 8.00 -2.02
## imean_posaff 2 30 3.78 0.71 3.91 3.76 0.56 2.61 5.62 3.01 0.29
## isd_posaff 3 30 0.88 0.26 0.87 0.87 0.26 0.32 1.52 1.20 0.17
## iskew_posaff 4 30 -0.15 0.46 -0.24 -0.19 0.46 -0.74 0.97 1.71 0.69
## ikurt_posaff 5 30 -0.79 0.50 -0.88 -0.84 0.47 -1.43 0.58 2.01 0.94
## ientropy_stress 6 30 1.47 0.28 1.50 1.48 0.28 0.84 1.90 1.06 -0.39
## kurtosis se
## icount_posaff 2.28 0.47
## imean_posaff -0.17 0.13
## isd_posaff -0.19 0.05
## iskew_posaff -0.45 0.08
## ikurt_posaff 0.01 0.09
## ientropy_stress -0.77 0.05Examine correlations
round(cor(istats_univariate[ ,-1], use="pairwise.complete.obs"),2)## icount_posaff imean_posaff isd_posaff iskew_posaff ikurt_posaff
## icount_posaff 1.00 0.08 -0.32 0.16 0.24
## imean_posaff 0.08 1.00 -0.45 -0.38 0.14
## isd_posaff -0.32 -0.45 1.00 0.21 -0.07
## iskew_posaff 0.16 -0.38 0.21 1.00 0.29
## ikurt_posaff 0.24 0.14 -0.07 0.29 1.00
## ientropy_stress -0.06 -0.24 0.29 -0.21 -0.11
## ientropy_stress
## icount_posaff -0.06
## imean_posaff -0.24
## isd_posaff 0.29
## iskew_posaff -0.21
## ikurt_posaff -0.11
## ientropy_stress 1.00Merge the univariate IIV metrics with other person-level data.
AMIB_univariate <- merge(istats_univariate, AMIB_persons, by="id")Examine relation between positive affect variability and neuroticism.
Look at association between isd_posaff and bfi_n:
#pdf("Figure1_UnivariateIIV.pdf",height=5.75, width=9)
ggplot(data=AMIB_univariate, aes(x=bfi_n, y=isd_posaff)) +
geom_point(colour="gray40") +
geom_smooth(aes(group=1), method=lm, se=TRUE, fullrange=TRUE, lty=1, size=2, color="#9A23DE") +
scale_y_continuous(breaks=c(0.4, 0.8, 1.2, 1.6), limits=c(0.32,1.6)) +
xlab("Neuroticism") + ylab("Positive Affect Variability") +
theme_classic() +
theme(axis.title=element_text(size=16),
axis.text=element_text(size=12),
plot.title=element_text(size=16, hjust=.5, face="bold")) +
ggtitle("Between-Person Association Univariate IIV")## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 1 rows containing non-finite values (stat_smooth).## Warning: Removed 1 rows containing missing values (geom_point).
#dev.off()And the formal model test (cross-sectional regression).
reg_univariate <- lm(isd_posaff ~ bfi_n,
data=AMIB_univariate,
na.action = na.exclude)
summary(reg_univariate)##
## Call:
## lm(formula = isd_posaff ~ bfi_n, data = AMIB_univariate, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49597 -0.14662 -0.00169 0.18189 0.49217
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.59383 0.15329 3.874 0.000589 ***
## bfi_n 0.08654 0.04499 1.923 0.064654 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.252 on 28 degrees of freedom
## Multiple R-squared: 0.1167, Adjusted R-squared: 0.08516
## F-statistic: 3.699 on 1 and 28 DF, p-value: 0.06465- For the prototypical person, positive affect variability is expected to be 0.59
- Individuals who are higher on neuroticism tend to have more variability in their positive affect. For every unit increase in neuroticism, characteristic positive affect is expected to increase by 0.09 (however, this association is not statistically significantly different from zero p = 0.06).
B. Bivariate IIV Metrics
There are are also several types of bivariate IIV metrics, including the iCorr, iCov, iPulse, iSpin, and iEntropy. The slope parameter from a within-person regression can, along with the iCorr and iCov also be considered a measure of intraindividual covariation.
We illustrate just a few of these. Again, the general principle is to use the functions in the plyr package to split the data by “id” and summarize each person’s data using a specific fucntion (e.g., cor, lm).
Calculate intraindiviudal correlation (iCor) and intraindividual covariance (iCov) and intraindividual regression (iReg):
istats_bivariate <- ddply(AMIB_daily, "id", summarize,
icor_affect = cor(x=posaff,y=negaff,
use="pairwise.complete.obs", method="pearson"),
icov_affect = cov(x=posaff,y=negaff,
use="pairwise.complete.obs", method="pearson"),
ireg_affect = coef(lm(posaff ~ negaff, na.action=na.exclude))[2])Look at bivariate IIV metrics data
round(head(istats_bivariate),2)## id icor_affect icov_affect ireg_affect
## 1 203 -0.63 -0.29 -0.98
## 2 204 -0.77 -1.18 -0.70
## 3 205 -0.44 -0.17 -0.53
## 4 208 -0.35 -0.06 -0.88
## 5 211 -0.08 -0.02 -0.17
## 6 214 -0.85 -0.83 -0.89Describe the bivariate IIV metrics
describe(istats_bivariate[ ,-1])## vars n mean sd median trimmed mad min max range skew
## icor_affect 1 30 -0.49 0.27 -0.54 -0.50 0.32 -0.90 0.01 0.91 0.30
## icov_affect 2 30 -0.39 0.41 -0.25 -0.32 0.31 -1.73 0.01 1.74 -1.61
## ireg_affect 3 30 -0.58 0.35 -0.62 -0.58 0.43 -1.21 0.03 1.24 0.03
## kurtosis se
## icor_affect -1.24 0.05
## icov_affect 2.28 0.07
## ireg_affect -1.20 0.06Correlations among the bivariate IIV metrics
round(cor(istats_bivariate[ ,-1], use="pairwise.complete.obs"),2)## icor_affect icov_affect ireg_affect
## icor_affect 1.00 0.73 0.84
## icov_affect 0.73 1.00 0.51
## ireg_affect 0.84 0.51 1.00Note the overlap between the iCor, iCov, and iReg metrics. This will be relevant when extending the iReg into the multilevel modeling framework - to examine between-person differences in intraindividual covariation.
Merge the bivariate IIV metrics with other person-level data.
AMIB_bivariate <- merge(istats_bivariate, AMIB_persons, by="id")Examine relation between Affect Bipolarity and neuroticism.
Look at association between isd_posaff and bfi_e:
#pdf("Figure2_BivariateIIV.pdf",height=3, width=9)
ggplot(data=AMIB_bivariate, aes(x=bfi_n, y=icor_affect)) +
geom_point(colour="gray40") +
geom_smooth(aes(group=1), method=lm, se=TRUE, fullrange=TRUE, lty=1, size=2, color="#9A23DE") +
xlab("Neuroticism") + ylab("Affect Bipolarity") +
theme_classic() +
theme(axis.title=element_text(size=16),
axis.text=element_text(size=12),
plot.title=element_text(size=16, hjust=.5, face="bold")) +
ggtitle("Between-Person Association Bivariate IIV")## `geom_smooth()` using formula 'y ~ x'
#dev.off()Fit model with the neuroticism predicting the individual slope score for the association between positive and negative affect.
reg_bivariate <- lm(icor_affect ~ bfi_n,
data=AMIB_bivariate,
na.action = na.exclude)
summary(reg_bivariate)##
## Call:
## lm(formula = icor_affect ~ bfi_n, data = AMIB_bivariate, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42499 -0.20524 -0.05017 0.24066 0.51684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.42619 0.16959 -2.513 0.018 *
## bfi_n -0.01979 0.04978 -0.398 0.694
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2788 on 28 degrees of freedom
## Multiple R-squared: 0.005616, Adjusted R-squared: -0.0299
## F-statistic: 0.1581 on 1 and 28 DF, p-value: 0.6939- For the prototypical person, affect bipolarity score for the sample is -0.43
- Individuals who are higher on neuroticism tend to have stronger affect bipolarity (scores further from zero). For every unit increase in neuroticism, affect bipolarity is expected to change by -0.02 (however, this association is not statistically significantly different from zero p = 0.69).
C. Multivariate IIV Metrics
Calculation of intraindividual variability metrics can be extended to multivariate time-series. Continuous measures can be summarized as a correlation/covariance matrix (and vector of means) - which in turn is summarized using metrics such as the determinant, Frobenius norm, or number of eigenvalues > 1 (Kaiser rule). Categorical measures can be summarized as a frequency table - which is, in turn, summarized using metrics such as Gini coefficient, richness, Shannon’s entropy, and Simpson’s index.
Calculating multivariate IIV metrics.
First, set the variables of interest (be sure the id variable is included in the first position)
vars <- c("id", "enthusiastic", "happy", "proud", "relaxed", "calm",
"sluggish", "sad", "disappointed", "angry", "nervous") Calculate the metrics. Each one takes a few steps
# remove ID 218 (due to zero variance in several items)
AMIB_daily_sub <- AMIB_daily[AMIB_daily$id!=218, ]
#calculating the determinant for each individual
istat_idet <- ddply(AMIB_daily_sub[ ,vars], "id",
function(x) {
det(cor(x[,-1],use="pairwise.complete.obs",
method="pearson"))} )
#renaming columns
colnames(istat_idet) <- c("id","idet")
#calculating Frobenius norm for each individual
istat_iFnorm <- ddply(AMIB_daily_sub[ ,vars], "id",
function(x) {
norm(cor(x[,-1],use="pairwise.complete.obs",
method="pearson"),type="F")} )
#renaming columns
colnames(istat_iFnorm) <- c("id","iFnorm")Merging all together
istats_multivar <- merge(istat_idet,istat_iFnorm, by="id")Look at multivariate IIV metrics data
round(head(istats_multivar),2)## id idet iFnorm
## 1 203 0.00 5.64
## 2 204 0.00 5.11
## 3 205 0.03 4.01
## 4 208 0.00 4.43
## 5 211 0.00 4.72
## 6 214 0.00 4.92Describe the bivariate IIV metrics.
describe(istats_multivar[ ,-1])## vars n mean sd median trimmed mad min max range skew kurtosis se
## idet 1 29 0.01 0.01 0.00 0.00 0.00 0.00 0.04 0.04 2.00 2.94 0.00
## iFnorm 2 29 4.89 0.65 4.89 4.83 0.56 3.97 6.98 3.01 1.04 1.66 0.12Correlations among the bivariate IIV metrics
round(cor(istats_multivar[ ,-1], use="pairwise.complete.obs"),2)## idet iFnorm
## idet 1.00 -0.64
## iFnorm -0.64 1.00Merge the multivariate IIV metrics with other person-level data.
AMIB_multivariate <- merge(istats_multivar, AMIB_persons, by="id")Examine relation between emotion system variability and neuroticism.
Look at association between idet and bfi_n:
#pdf("Figure3_MultivariateIIV.pdf",height=3, width=5.45)
ggplot(data=AMIB_multivariate, aes(x=bfi_n, y=idet)) +
geom_point(colour="gray40") +
geom_smooth(aes(group=1), method="lm", se=TRUE, fullrange=TRUE, lty=1, size=2, color="#9A23DE") +
xlab("Neuroticism") + ylab("Emotion System\nVariability") +
theme_classic() +
theme(axis.title=element_text(size=16),
axis.text=element_text(size=12),
plot.title=element_text(size=16, hjust=.5)) +
ggtitle("Between-Person Association Multivariate IIV")## `geom_smooth()` using formula 'y ~ x'