APIM & APIMeM
Jeong Eun Cheon
cheonje@yonsei.ac.krPreparing for the analysis
Read in data
## Warning: package 'ggplot2' was built under R version 4.3.2Using data from Cultice et al. (2022), we will explore path analysis alongside the APIM and APIMeM models (i.e., actor-partner interdependence mediation model; Ledermann et al., 2011), aiming to replicate their findings.
- References:
Cultice, R. A., Sanchez, D. T., & Albuja, A. F. (2022). Sexual growth mindsets and rejection sensitivity in sexual satisfaction. Journal of Social and Personal Relationships, 39(4), 1131-1153. https://doi.org/10.1177/02654075211054390
Ledermann, T., Macho, S., & Kenny, D. A. (2011). Assessing mediation in dyadic data using the actor-partner interdependence model. Structural Equation Modeling: A Multidisciplinary Journal, 18(4), 595-612. https://doi.org/10.1080/10705511.2011.607099
Basics
- multivariate normality
- outlier
- collinearity
- reliability
- missing
multivariate normality
The Maximum Likelihood (ML) method is the most commonly used for Structural Equation Modeling (SEM) and it is often presumed that all continuous variables in the model are normally distributed across their multivariate relationship. However, when this assumption of multivariate normality isn’t met, as might be the case if some continuous variables exhibit skewness or kurtosis, it can lead to inaccurate results if ML is applied without adjustments. Specifically, the standard errors associated with the model’s parameters may be underestimated, which could result in an increased risk of Type I errors (incorrectly rejecting a true null hypothesis). The estimated values of the model parameters themselves, such as factor loadings, path coefficients, and correlations, can remain stable even when normality is not present.
Evaluating normality in data, crucial for many statistical analyses, involves checking both the univariate and multivariate normality (multivariate normality is related to univariate normality). For univariate assessments, it is important to look for outliers, skewness, and kurtosis in the distribution of each variable. When it comes to multivariate distributions, people commonly investigate Mardia’s Coefficient (scores above 3.00 suggest a deviation from normality) and Mahalanobis Distance/Cook’s distance.
options: QQplot, Shaprio-Wilk, skewness, kurtosis …
-West, Finch, & Curran (1995) suggest that skewness > 2 and kurtosis > 7 indicate nonnormality. Kline(2011): skewness > 3, kurtosis > 10 -z test Z_skewness = (Skewness / SE_skewness) Z_kurtosis = (Kurtosis / SE_kurtosis) skew/SE< |1.96|, kurtosis/SE< |1.96| skew/SE< |2|, kurtosis/SE< |2|
also refer to: https://centerstat.org/can-i-estimate-an-sem-if-the-sample-data-are-not-normally-distributed/#:~:text=First%2C%20the%20assumption%20of%20normality,likelihood%20(ML)%20estimator%20does.
qqnorm(Study1$SexSatisfaction, pch = 1, frame = FALSE)
qqline(Study1$SexSatisfaction, col = "steelblue", lwd = 2)
##
## Shapiro-Wilk normality test
##
## data: Study1$SexSatisfaction
## W = 0.77517, p-value < 0.00000000000000022##
## Shapiro-Wilk normality test
##
## data: Study1$SexSatisfaction
## W = 0.77517, p-value < 0.00000000000000022## Warning: package 'mvnormalTest' was built under R version 4.3.3## $mv.test
## Test Statistic p-value Result
## 1 Skewness 197.7441 0 NO
## 2 Kurtosis 13.3237 0 NO
## 3 MV Normality <NA> <NA> NO
##
## $uv.shapiro
## W p-value UV.Normality
## statistic 0.7752 0 No## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 375 6.12 1.14 6.6 6.34 0.59 1 7 6 -1.77 3.32 0.06
yet… Lei and Lomax (2005) explored the impact of nonnormality in structural equation modeling (SEM) and found that the condition of nonnormality doesn’t notably affect the standard errors of parameter estimates across different sample sizes or estimation methods. Notably, standard errors for dependent variables were consistently lower than those for independent variables, implying that estimates for dependent variables tend to be more precise. While sample size and estimation method (whether Maximum Likelihood or Generalized Least Squares) showed minimal influence on the bias of parameter estimates for independent variables, they did have an impact on dependent variables, with larger samples leading to reduced bias in parameter estimates. Additionally, nonnormality affected parameter estimates more significantly in smaller samples.
reference:
Lei, M., & Lomax, R. G. (2005). The effect of varying degrees of nonnormality in structural equation modeling. Structural equation modeling, 12(1), 1-27. https://doi.org/10.1207/s15328007sem1201_1
outlier
out <- boxplot.stats(Study1$Growth)$out
out_ind <- which(Study1$Growth %in% c(out)) #extract the row number corresponding to outliers
out_ind## integer(0)## Warning: package 'performance' was built under R version 4.3.2## OK: No outliers detected.
## - Based on the following method and threshold: zscore_robust (3.291).
## - For variable: Study1$Growth# or calculate how many standard deviations it falls from the mean.
mean_growth <- mean(Study1$Growth, na.rm = TRUE)
sd_growth <- sd(Study1$Growth, na.rm = TRUE)
# Calculate the z-scores
z_scores <- abs((Study1$Growth - mean_growth) / sd_growth)
# Identify outliers
outliers <- z_scores > 3
# Subset the dataset to remove outliers
#Study1_no_outliers <- Study1[!outliers, ]
#filtered <- subset(Study1, Study1$Growth > 3)collinearity
## Call:corr.test(x = Study1[c("Growth", "Growth_Partner")])
## Correlation matrix
## Growth Growth_Partner
## Growth 1.00 0.77
## Growth_Partner 0.77 1.00
## Sample Size
## Growth Growth_Partner
## Growth 375 374
## Growth_Partner 374 374
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Growth Growth_Partner
## Growth 0 0
## Growth_Partner 0 0
##
## To see confidence intervals of the correlations, print with the short=FALSE optionreliaiblity
##
## Reliability analysis
## Call: alpha(x = Study1[, c("Growth", "Growth_Partner")])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.87 0.87 0.77 0.77 6.7 0.013 4.5 1.4 0.77
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.84 0.87 0.89
## Duhachek 0.84 0.87 0.90
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Growth 0.74 0.77 0.59 0.77 3.4 NA 0 0.77
## Growth_Partner 0.80 0.77 0.59 0.77 3.4 NA 0 0.77
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Growth 375 0.94 0.94 0.83 0.77 4.6 1.5
## Growth_Partner 374 0.94 0.94 0.83 0.77 4.5 1.5missing
## [1] 2## Mode FALSE TRUE
## logical 375 2There are several ways to deal with missing values
Listwise deletion: Involves removing any cases (rows) with missing values in any variable from the analysis.
Full Information Maximum Likelihood (FIML): FIML is an approach directly incorporated into the estimation process of SEM that uses all available data to estimate model parameters without needing to impute missing values beforehand. It operates under the assumption that data are missing at random (MAR), meaning that the probability of missing data on a variable is related to other observed variables but not to the values of the variable itself.
Multiple Imputation (MI): Multiple Imputation involves replacing each missing value with a set of plausible values to generate multiple complete datasets.
Study 1
Path analysis: Replicating Cultice et al. (2022) Study 1’s findings
library(lavaan)
Study1model <- 'SexSatisfaction ~ Rejection
SexSatisfaction ~ Rejection_Partner
Rejection ~ Growth
Rejection ~ Growth_Partner
Rejection_Partner ~ Growth_Partner
Rejection_Partner ~ Growth
Growth ~~ Growth_Partner
Rejection ~~ Rejection_Partner
'
Study1modelout <- sem(Study1model, data=Study1, test="bootstrap", bootstrap=100)
summary(Study1modelout, fit.measures = TRUE, standardize=TRUE, rsquare=TRUE, ci = TRUE)## lavaan 0.6.16 ended normally after 26 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Used Total
## Number of observations 374 377
##
## Model Test User Model:
##
## Test statistic 1.957
## Degrees of freedom 2
## P-value (Chi-square) 0.376
##
## Test statistic 1.957
## Degrees of freedom 2
## P-value (Bollen-Stine bootstrap) 0.430
##
## Model Test Baseline Model:
##
## Test statistic 570.772
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3587.638
## Loglikelihood unrestricted model (H1) -3586.659
##
## Akaike (AIC) 7201.276
## Bayesian (BIC) 7252.291
## Sample-size adjusted Bayesian (SABIC) 7211.046
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.102
## P-value H_0: RMSEA <= 0.050 0.647
## P-value H_0: RMSEA >= 0.080 0.137
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.008
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## SexSatisfaction ~
## Rejection -0.067 0.011 -6.397 0.000 -0.088 -0.047
## Rejectin_Prtnr -0.020 0.039 -0.496 0.620 -0.097 0.058
## Rejection ~
## Growth -0.247 0.324 -0.762 0.446 -0.881 0.388
## Growth_Partner -1.030 0.311 -3.309 0.001 -1.640 -0.420
## Rejection_Partner ~
## Growth_Partner -0.245 0.084 -2.905 0.004 -0.410 -0.080
## Growth -0.049 0.088 -0.554 0.579 -0.220 0.123
## Std.lv Std.all
##
## -0.067 -0.364
## -0.020 -0.028
##
## -0.247 -0.059
## -1.030 -0.256
##
## -0.245 -0.228
## -0.049 -0.043
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Growth ~~
## Growth_Partner 1.739 0.147 11.813 0.000 1.450 2.027
## .Rejection ~~
## .Rejectin_Prtnr 4.684 0.539 8.692 0.000 3.628 5.740
## Std.lv Std.all
##
## 1.739 0.771
##
## 4.684 0.503
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfactin 1.110 0.081 13.675 0.000 0.951 1.269
## .Rejection 34.352 2.512 13.675 0.000 29.429 39.276
## .Rejectin_Prtnr 2.523 0.185 13.675 0.000 2.161 2.885
## Growth 2.168 0.159 13.675 0.000 1.857 2.479
## Growth_Partner 2.343 0.171 13.675 0.000 2.008 2.679
## Std.lv Std.all
## 1.110 0.855
## 34.352 0.908
## 2.523 0.931
## 2.168 1.000
## 2.343 1.000
##
## R-Square:
## Estimate
## SexSatisfactin 0.145
## Rejection 0.092
## Rejectin_Prtnr 0.069## npar fmin chisq
## 13.000 0.003 1.957
## df pvalue baseline.chisq
## 2.000 0.376 570.772
## baseline.df baseline.pvalue cfi
## 10.000 0.000 1.000
## tli nnfi rfi
## 1.000 1.000 0.983
## nfi pnfi ifi
## 0.997 0.199 1.000
## rni logl unrestricted.logl
## 1.000 -3587.638 -3586.659
## aic bic ntotal
## 7201.276 7252.291 374.000
## bic2 rmsea rmsea.ci.lower
## 7211.046 0.000 0.000
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.102 0.900 0.647
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 0.137 0.080
## rmr rmr_nomean srmr
## 0.014 0.014 0.008
## srmr_bentler srmr_bentler_nomean crmr
## 0.008 0.008 0.010
## crmr_nomean srmr_mplus srmr_mplus_nomean
## 0.010 0.008 0.008
## cn_05 cn_01 gfi
## 1145.840 1760.897 0.998
## agfi pgfi mfi
## 0.984 0.133 1.000
## ecvi
## 0.075library(lavaan)
Study1model2 <- 'SexSatisfaction ~ a2*Rejection
SexSatisfaction ~ p2*Rejection_Partner
Rejection ~ a1*Growth
Rejection ~ ap1*Growth_Partner
Rejection_Partner ~ p1*Growth_Partner
Rejection_Partner ~ pa1*Growth
Growth ~~ Growth_Partner
Rejection ~~ Rejection_Partner
ind1 := a1*a2
ind2 := p1*p2
ind3 := ap1*p2
ind4 := pa1*a2
'
Study1model2out <- sem(Study1model2, data=Study1, test="bootstrap", bootstrap=100)
summary(Study1model2out, fit.measures = TRUE, standardize=TRUE, rsquare=TRUE, ci = TRUE)## lavaan 0.6.16 ended normally after 26 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Used Total
## Number of observations 374 377
##
## Model Test User Model:
##
## Test statistic 1.957
## Degrees of freedom 2
## P-value (Chi-square) 0.376
##
## Test statistic 1.957
## Degrees of freedom 2
## P-value (Bollen-Stine bootstrap) 0.380
##
## Model Test Baseline Model:
##
## Test statistic 570.772
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3587.638
## Loglikelihood unrestricted model (H1) -3586.659
##
## Akaike (AIC) 7201.276
## Bayesian (BIC) 7252.291
## Sample-size adjusted Bayesian (SABIC) 7211.046
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.102
## P-value H_0: RMSEA <= 0.050 0.647
## P-value H_0: RMSEA >= 0.080 0.137
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.008
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## SexSatisfaction ~
## Rejectin (a2) -0.067 0.011 -6.397 0.000 -0.088 -0.047
## Rjctn_Pr (p2) -0.020 0.039 -0.496 0.620 -0.097 0.058
## Rejection ~
## Growth (a1) -0.247 0.324 -0.762 0.446 -0.881 0.388
## Grwth_Pr (ap1) -1.030 0.311 -3.309 0.001 -1.640 -0.420
## Rejection_Partner ~
## Grwth_Pr (p1) -0.245 0.084 -2.905 0.004 -0.410 -0.080
## Growth (pa1) -0.049 0.088 -0.554 0.579 -0.220 0.123
## Std.lv Std.all
##
## -0.067 -0.364
## -0.020 -0.028
##
## -0.247 -0.059
## -1.030 -0.256
##
## -0.245 -0.228
## -0.049 -0.043
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Growth ~~
## Growth_Partner 1.739 0.147 11.813 0.000 1.450 2.027
## .Rejection ~~
## .Rejectin_Prtnr 4.684 0.539 8.692 0.000 3.628 5.740
## Std.lv Std.all
##
## 1.739 0.771
##
## 4.684 0.503
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfactin 1.110 0.081 13.675 0.000 0.951 1.269
## .Rejection 34.352 2.512 13.675 0.000 29.429 39.276
## .Rejectin_Prtnr 2.523 0.185 13.675 0.000 2.161 2.885
## Growth 2.168 0.159 13.675 0.000 1.857 2.479
## Growth_Partner 2.343 0.171 13.675 0.000 2.008 2.679
## Std.lv Std.all
## 1.110 0.855
## 34.352 0.908
## 2.523 0.931
## 2.168 1.000
## 2.343 1.000
##
## R-Square:
## Estimate
## SexSatisfactin 0.145
## Rejection 0.092
## Rejectin_Prtnr 0.069
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ind1 0.017 0.022 0.757 0.449 -0.026 0.060
## ind2 0.005 0.010 0.489 0.625 -0.014 0.024
## ind3 0.020 0.041 0.490 0.624 -0.060 0.101
## ind4 0.003 0.006 0.552 0.581 -0.008 0.015
## Std.lv Std.all
## 0.017 0.021
## 0.005 0.006
## 0.020 0.007
## 0.003 0.016## npar fmin chisq
## 13.000 0.003 1.957
## df pvalue baseline.chisq
## 2.000 0.376 570.772
## baseline.df baseline.pvalue cfi
## 10.000 0.000 1.000
## tli nnfi rfi
## 1.000 1.000 0.983
## nfi pnfi ifi
## 0.997 0.199 1.000
## rni logl unrestricted.logl
## 1.000 -3587.638 -3586.659
## aic bic ntotal
## 7201.276 7252.291 374.000
## bic2 rmsea rmsea.ci.lower
## 7211.046 0.000 0.000
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.102 0.900 0.647
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 0.137 0.080
## rmr rmr_nomean srmr
## 0.014 0.014 0.008
## srmr_bentler srmr_bentler_nomean crmr
## 0.008 0.008 0.010
## crmr_nomean srmr_mplus srmr_mplus_nomean
## 0.010 0.008 0.008
## cn_05 cn_01 gfi
## 1145.840 1760.897 0.998
## agfi pgfi mfi
## 0.984 0.133 1.000
## ecvi
## 0.075standardizedSolution(Study1model2out, type = "std.all", se = TRUE, zstat = TRUE,
pvalue = TRUE, ci = TRUE, level = 0.95)## lhs op rhs label est.std se z pvalue
## 1 SexSatisfaction ~ Rejection a2 -0.364 0.054 -6.719 0.000
## 2 SexSatisfaction ~ Rejection_Partner p2 -0.028 0.057 -0.496 0.620
## 3 Rejection ~ Growth a1 -0.059 0.077 -0.763 0.446
## 4 Rejection ~ Growth_Partner ap1 -0.256 0.076 -3.354 0.001
## 5 Rejection_Partner ~ Growth_Partner p1 -0.228 0.078 -2.936 0.003
## 6 Rejection_Partner ~ Growth pa1 -0.043 0.078 -0.555 0.579
## 7 Growth ~~ Growth_Partner 0.771 0.021 36.857 0.000
## 8 Rejection ~~ Rejection_Partner 0.503 0.039 13.027 0.000
## 9 SexSatisfaction ~~ SexSatisfaction 0.855 0.034 25.434 0.000
## 10 Rejection ~~ Rejection 0.908 0.029 31.799 0.000
## 11 Rejection_Partner ~~ Rejection_Partner 0.931 0.025 36.792 0.000
## 12 Growth ~~ Growth 1.000 0.000 NA NA
## 13 Growth_Partner ~~ Growth_Partner 1.000 0.000 NA NA
## 14 ind1 := a1*a2 ind1 0.021 0.028 0.757 0.449
## 15 ind2 := p1*p2 ind2 0.006 0.013 0.489 0.625
## 16 ind3 := ap1*p2 ind3 0.007 0.015 0.491 0.624
## 17 ind4 := pa1*a2 ind4 0.016 0.029 0.553 0.581
## ci.lower ci.upper
## 1 -0.470 -0.258
## 2 -0.140 0.083
## 3 -0.211 0.093
## 4 -0.406 -0.107
## 5 -0.380 -0.076
## 6 -0.197 0.110
## 7 0.730 0.813
## 8 0.427 0.579
## 9 0.790 0.921
## 10 0.852 0.963
## 11 0.881 0.981
## 12 1.000 1.000
## 13 1.000 1.000
## 14 -0.034 0.077
## 15 -0.019 0.032
## 16 -0.022 0.036
## 17 -0.040 0.072Controling for sexual frequency
Study1model3 <- 'SexSatisfaction ~ a2*Rejection
SexSatisfaction ~ p2*Rejection_Partner
Rejection ~ a1*Growth
Rejection ~ ap1*Growth_Partner
Rejection_Partner ~ p1*Growth_Partner
Rejection_Partner ~ pa1*Growth
Growth ~~ Growth_Partner
Rejection ~~ Rejection_Partner
Rejection ~ SexFrequency
Rejection_Partner ~ SexFrequency
SexSatisfaction ~ SexFrequency
Growth ~~ SexFrequency
Growth_Partner ~~ SexFrequency
ind1 := a1*a2
ind2 := p1*p2
ind3 := ap1*a2
ind4 := pa1*p2
'
Study1model3out <- sem(Study1model3, data=Study1, test="bootstrap", bootstrap=100)
summary(Study1model3out, fit.measures = TRUE, standardize=TRUE, rsquare=TRUE, ci = TRUE)## lavaan 0.6.16 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
##
## Used Total
## Number of observations 361 377
##
## Model Test User Model:
##
## Test statistic 1.881
## Degrees of freedom 2
## P-value (Chi-square) 0.390
##
## Test statistic 1.881
## Degrees of freedom 2
## P-value (Bollen-Stine bootstrap) 0.470
##
## Model Test Baseline Model:
##
## Test statistic 556.672
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4419.388
## Loglikelihood unrestricted model (H1) -4418.447
##
## Akaike (AIC) 8876.775
## Bayesian (BIC) 8950.664
## Sample-size adjusted Bayesian (SABIC) 8890.386
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.102
## P-value H_0: RMSEA <= 0.050 0.652
## P-value H_0: RMSEA >= 0.080 0.138
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.007
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## SexSatisfaction ~
## Rejectin (a2) -0.063 0.011 -6.040 0.000 -0.084 -0.043
## Rjctn_Pr (p2) -0.017 0.040 -0.435 0.663 -0.095 0.060
## Rejection ~
## Growth (a1) -0.323 0.326 -0.989 0.323 -0.963 0.317
## Grwth_Pr (ap1) -0.985 0.313 -3.149 0.002 -1.598 -0.372
## Rejection_Partner ~
## Grwth_Pr (p1) -0.228 0.085 -2.690 0.007 -0.393 -0.062
## Growth (pa1) -0.045 0.088 -0.508 0.611 -0.218 0.128
## Rejection ~
## SxFrqncy -0.247 0.087 -2.832 0.005 -0.418 -0.076
## Rejection_Partner ~
## SxFrqncy -0.009 0.024 -0.401 0.688 -0.056 0.037
## SexSatisfaction ~
## SxFrqncy 0.041 0.015 2.684 0.007 0.011 0.072
## Std.lv Std.all
##
## -0.063 -0.349
## -0.017 -0.025
##
## -0.323 -0.077
## -0.985 -0.243
##
## -0.228 -0.213
## -0.045 -0.040
##
## -0.247 -0.142
##
## -0.009 -0.021
##
## 0.041 0.131
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Growth ~~
## Growth_Partner 1.712 0.148 11.544 0.000 1.421 2.003
## .Rejection ~~
## .Rejectin_Prtnr 4.685 0.545 8.597 0.000 3.617 5.753
## Growth ~~
## SexFrequency -0.581 0.275 -2.109 0.035 -1.121 -0.041
## Growth_Partner ~~
## SexFrequency -0.458 0.286 -1.602 0.109 -1.019 0.102
## Std.lv Std.all
##
## 1.712 0.765
##
## 4.685 0.507
##
## -0.581 -0.112
##
## -0.458 -0.085
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfactin 1.059 0.079 13.435 0.000 0.905 1.214
## .Rejection 34.143 2.541 13.435 0.000 29.162 39.124
## .Rejectin_Prtnr 2.497 0.186 13.435 0.000 2.133 2.861
## Growth 2.151 0.160 13.435 0.000 1.837 2.465
## Growth_Partner 2.329 0.173 13.435 0.000 1.989 2.669
## SexFrequency 12.581 0.936 13.435 0.000 10.746 14.416
## Std.lv Std.all
## 1.059 0.841
## 34.143 0.895
## 2.497 0.940
## 2.151 1.000
## 2.329 1.000
## 12.581 1.000
##
## R-Square:
## Estimate
## SexSatisfactin 0.159
## Rejection 0.105
## Rejectin_Prtnr 0.060
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ind1 0.020 0.021 0.976 0.329 -0.021 0.062
## ind2 0.004 0.009 0.430 0.667 -0.014 0.022
## ind3 0.063 0.022 2.792 0.005 0.019 0.106
## ind4 0.001 0.002 0.331 0.741 -0.004 0.005
## Std.lv Std.all
## 0.020 0.027
## 0.004 0.005
## 0.063 0.085
## 0.001 0.001## npar fmin chisq
## 19.000 0.003 1.881
## df pvalue baseline.chisq
## 2.000 0.390 556.672
## baseline.df baseline.pvalue cfi
## 15.000 0.000 1.000
## tli nnfi rfi
## 1.002 1.002 0.975
## nfi pnfi ifi
## 0.997 0.133 1.000
## rni logl unrestricted.logl
## 1.000 -4419.388 -4418.447
## aic bic ntotal
## 8876.775 8950.664 361.000
## bic2 rmsea rmsea.ci.lower
## 8890.386 0.000 0.000
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.102 0.900 0.652
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 0.138 0.080
## rmr rmr_nomean srmr
## 0.012 0.012 0.007
## srmr_bentler srmr_bentler_nomean crmr
## 0.007 0.007 0.008
## crmr_nomean srmr_mplus srmr_mplus_nomean
## 0.008 0.007 0.007
## cn_05 cn_01 gfi
## 1150.832 1768.572 0.998
## agfi pgfi mfi
## 0.982 0.095 1.000
## ecvi
## 0.110## lhs op rhs label est se z pvalue
## 1 SexSatisfaction ~ Rejection a2 -0.063 0.011 -6.040 0.000
## 2 SexSatisfaction ~ Rejection_Partner p2 -0.017 0.040 -0.435 0.663
## 3 Rejection ~ Growth a1 -0.323 0.326 -0.989 0.323
## 4 Rejection ~ Growth_Partner ap1 -0.985 0.313 -3.149 0.002
## 5 Rejection_Partner ~ Growth_Partner p1 -0.228 0.085 -2.690 0.007
## 6 Rejection_Partner ~ Growth pa1 -0.045 0.088 -0.508 0.611
## 7 Growth ~~ Growth_Partner 1.712 0.148 11.544 0.000
## 8 Rejection ~~ Rejection_Partner 4.685 0.545 8.597 0.000
## 9 Rejection ~ SexFrequency -0.247 0.087 -2.832 0.005
## 10 Rejection_Partner ~ SexFrequency -0.009 0.024 -0.401 0.688
## 11 SexSatisfaction ~ SexFrequency 0.041 0.015 2.684 0.007
## 12 Growth ~~ SexFrequency -0.581 0.275 -2.109 0.035
## 13 Growth_Partner ~~ SexFrequency -0.458 0.286 -1.602 0.109
## 14 SexSatisfaction ~~ SexSatisfaction 1.059 0.079 13.435 0.000
## 15 Rejection ~~ Rejection 34.143 2.541 13.435 0.000
## 16 Rejection_Partner ~~ Rejection_Partner 2.497 0.186 13.435 0.000
## 17 Growth ~~ Growth 2.151 0.160 13.435 0.000
## 18 Growth_Partner ~~ Growth_Partner 2.329 0.173 13.435 0.000
## 19 SexFrequency ~~ SexFrequency 12.581 0.936 13.435 0.000
## 20 ind1 := a1*a2 ind1 0.020 0.021 0.976 0.329
## 21 ind2 := p1*p2 ind2 0.004 0.009 0.430 0.667
## 22 ind3 := ap1*a2 ind3 0.063 0.022 2.792 0.005
## 23 ind4 := pa1*p2 ind4 0.001 0.002 0.331 0.741
## ci.lower ci.upper
## 1 -0.084 -0.043
## 2 -0.095 0.060
## 3 -0.963 0.317
## 4 -1.598 -0.372
## 5 -0.393 -0.062
## 6 -0.218 0.128
## 7 1.421 2.003
## 8 3.617 5.753
## 9 -0.418 -0.076
## 10 -0.056 0.037
## 11 0.011 0.072
## 12 -1.121 -0.041
## 13 -1.019 0.102
## 14 0.905 1.214
## 15 29.162 39.124
## 16 2.133 2.861
## 17 1.837 2.465
## 18 1.989 2.669
## 19 10.746 14.416
## 20 -0.021 0.062
## 21 -0.014 0.022
## 22 0.019 0.106
## 23 -0.004 0.005from Cultice et al. (2022), pages 1139-1140:
“Next, we tested the hypothesized model. The model indicated good fit, \(\chi^2\) (2, \(N = 361\)) = 1.88, \(p = .39\), CFI = 1.0, TLI = 1.0, RMSEA = .00, SRMR = .01, AIC = 8888.78 (see Figure 2). Greater perceived partner sexual growth mindset was associated with lower (own) sexual rejection sensitivity (\(\beta = -0.24, p = .002\)) and lower perceptions of partner’s rejection sensitivity (\(\beta = -0.21, p = .02\)). However, there was no relationship between participants’ own sexual growth mindset and own or perceived partner’s sexual rejection sensitivity. Further, the indirect effect from own sexual growth mindset to sexual satisfaction through rejection sensitivity was not significant, \(\beta = 0.03, p = .31, 95\% CI [-0.03, 0.08]\); however, the indirect effect from perceived partner sexual growth mindset to sexual satisfaction through rejection sensitivity was significant, \(\beta = 0.09, p = .006, 95\% CI [0.02, 0.15]\). This suggests that when both participants’ own and their perceived partner’s sexual growth mindset is considered, a person’s sexual rejection sensitivity is associated more strongly with how they perceive their partner’s sexual growth mindset, and less strongly with their own sexual growth mindset. Higher (own) sexual rejection sensitivity significantly predicted lower sexual satisfaction (\(\beta = -0.35, p < .001\)); however, the path from perceived partner’s sexual rejection sensitivity to sexual satisfaction did not. Finally, sexual frequency was associated with lower sexual rejection sensitivity and greater overall sexual satisfaction.”
- p.s. modification index
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 27 SexSatisfaction ~~ Growth_Partner 1.776 0.072 0.072 0.046 0.046
## 46 Growth_Partner ~ SexSatisfaction 1.776 0.068 0.068 0.050 0.050
## 26 SexSatisfaction ~~ Growth 1.538 -0.063 -0.063 -0.042 -0.042
## 41 Growth ~ SexSatisfaction 1.538 -0.060 -0.060 -0.046 -0.046
## 36 SexSatisfaction ~ Growth_Partner 0.361 0.023 0.023 0.031 0.031The MI value indicates the potential improvement in model fit if the specified parameter is added to the model. Higher values suggest greater potential for improvement.
Study2
Actor-partner interdependence model (APIM)
Let’s investigate whether sexual growth mindset is related to sexual satisfaction in couples.
Variable explanation
Growth_F = female sexual growth mindset Growth_M = male sexual growth mindset
SexSatisfaction_F = female sexual satisfaction SexSatisfaction_M = male sexual satisfaction
library(lavaan)
APIM <- 'SexSatisfaction_F ~ Growth_F
SexSatisfaction_F ~ Growth_M
SexSatisfaction_M ~ Growth_M
SexSatisfaction_M ~ Growth_F
'
APIMout <- sem(APIM, data=Study2)
summary(APIMout, fit.measures = TRUE, standardize=TRUE, rsquare=TRUE, ci = TRUE)## lavaan 0.6.16 ended normally after 19 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 104
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 96.197
## Degrees of freedom 5
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -242.501
## Loglikelihood unrestricted model (H1) -242.501
##
## Akaike (AIC) 499.002
## Bayesian (BIC) 517.513
## Sample-size adjusted Bayesian (SABIC) 495.400
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## SexSatisfaction_F ~
## Growth_F 0.020 0.085 0.240 0.810 -0.146 0.187
## Growth_M -0.023 0.083 -0.279 0.781 -0.185 0.139
## SexSatisfaction_M ~
## Growth_M 0.044 0.071 0.625 0.532 -0.095 0.183
## Growth_F -0.056 0.073 -0.760 0.447 -0.199 0.088
## Std.lv Std.all
##
## 0.020 0.029
## -0.023 -0.034
##
## 0.044 0.076
## -0.056 -0.092
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfaction_F ~~
## .SexSatisfctn_M 0.739 0.118 6.247 0.000 0.507 0.971
## Std.lv Std.all
##
## 0.739 0.775
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfctn_F 1.110 0.154 7.211 0.000 0.808 1.411
## .SexSatisfctn_M 0.820 0.114 7.211 0.000 0.597 1.043
## Std.lv Std.all
## 1.110 0.999
## 0.820 0.994
##
## R-Square:
## Estimate
## SexSatisfctn_F 0.001
## SexSatisfctn_M 0.006## npar fmin chisq
## 7.000 0.000 0.000
## df pvalue baseline.chisq
## 0.000 NA 96.197
## baseline.df baseline.pvalue cfi
## 5.000 0.000 1.000
## tli nnfi rfi
## 1.000 1.000 1.000
## nfi pnfi ifi
## 1.000 0.000 1.000
## rni logl unrestricted.logl
## 1.000 -242.501 -242.501
## aic bic ntotal
## 499.002 517.513 104.000
## bic2 rmsea rmsea.ci.lower
## 495.400 0.000 0.000
## rmsea.ci.upper rmsea.ci.level rmsea.pvalue
## 0.000 0.900 NA
## rmsea.close.h0 rmsea.notclose.pvalue rmsea.notclose.h0
## 0.050 NA 0.080
## rmr rmr_nomean srmr
## 0.000 0.000 0.000
## srmr_bentler srmr_bentler_nomean crmr
## 0.000 0.000 0.000
## crmr_nomean srmr_mplus srmr_mplus_nomean
## 0.000 0.000 0.000
## cn_05 cn_01 gfi
## 1.000 1.000 1.000
## agfi pgfi mfi
## 1.000 0.000 1.000
## ecvi
## 0.135In an Actor-Partner Interdependence Model (APIM) analysis of sexual satisfaction among 104 couples, sexual growth mindset was modeled as a predictor for both female and male partners’ reported sexual satisfaction.
The regression coefficients for the paths from sexual growth mindset to sexual satisfaction were not statistically significant for either partner. For females, the effect of their own growth on sexual satisfaction was estimated at \(\hat{\beta} = 0.020\), \(SE = 0.085\), \(z = 0.240\), \(p = .810\), and for the effect of male partners’ growth on female sexual satisfaction, \(\hat{\beta} = -0.023\), \(SE = 0.083\), \(z = -0.279\), \(p = .781\). For males, their own sexual growth mindset predicted sexual satisfaction with an estimate of \(\hat{\beta} = 0.044\), \(SE = 0.071\), \(z = 0.625\), \(p = .532\), and the effect of female sexual growth mindset on male sexual satisfaction was \(\hat{\beta} = -0.056\), \(SE = 0.073\), \(z = -0.760\), \(p = .447\).
The R-squared values indicated that the model explained 0.1% of the variance in female sexual satisfaction and 0.6% of the variance in male sexual satisfaction.
APIMeM
## Call:corr.test(x = Study2[c("SexFrequency_F", "SexFrequency_M")])
## Correlation matrix
## SexFrequency_F SexFrequency_M
## SexFrequency_F 1.00 0.91
## SexFrequency_M 0.91 1.00
## Sample Size
## [1] 104
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## SexFrequency_F SexFrequency_M
## SexFrequency_F 0 0
## SexFrequency_M 0 0
##
## To see confidence intervals of the correlations, print with the short=FALSE optionlibrary(lavaan)
Study1model4 <- 'SexSatisfaction_F ~ fa2*Rejection_F
SexSatisfaction_F ~ mp2*Rejection_M
SexSatisfaction_M ~ ma2*Rejection_M
SexSatisfaction_M ~ fp2*Rejection_F
Rejection_F ~ fa1*Growth_F
Rejection_F ~ mp1*Growth_M
Rejection_M ~ ma1*Growth_M
Rejection_M ~ fp1*Growth_F
Growth_M ~~ Growth_F
Rejection_M ~~ Rejection_F
SexSatisfaction_M ~~ SexSatisfaction_F
Rejection_M ~ SexFrequency_M
Rejection_F ~ SexFrequency_M
SexSatisfaction_M ~ SexFrequency_M
SexSatisfaction_F ~ SexFrequency_M
SexFrequency_M ~~ Growth_F
SexFrequency_M ~~ Growth_M
ind1 := fa1*fa2
ind2 := ma1*ma2
ind3 := fa1*fp2
ind4 := fp1*ma2
ind5 := mp1*fa2 # and so on...
'
Study1model4out <- sem(Study1model4, data=Study2, test="bootstrap", bootstrap=100)
summary(Study1model4out, fit.measures = TRUE, standardize=TRUE, rsquare=TRUE, ci = TRUE)## lavaan 0.6.16 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Number of observations 104
##
## Model Test User Model:
##
## Test statistic 5.045
## Degrees of freedom 4
## P-value (Chi-square) 0.283
##
## Test statistic 5.045
## Degrees of freedom 4
## P-value (Bollen-Stine bootstrap) 0.250
##
## Model Test Baseline Model:
##
## Test statistic 263.212
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.996
## Tucker-Lewis Index (TLI) 0.977
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1320.895
## Loglikelihood unrestricted model (H1) -1318.373
##
## Akaike (AIC) 2689.790
## Bayesian (BIC) 2753.255
## Sample-size adjusted Bayesian (SABIC) 2677.439
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.050
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.163
## P-value H_0: RMSEA <= 0.050 0.409
## P-value H_0: RMSEA >= 0.080 0.423
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## SexSatisfaction_F ~
## Rejctn_F (fa2) -0.047 0.020 -2.427 0.015 -0.086 -0.009
## Rejctn_M (mp2) -0.034 0.019 -1.787 0.074 -0.071 0.003
## SexSatisfaction_M ~
## Rejctn_M (ma2) -0.039 0.016 -2.357 0.018 -0.071 -0.007
## Rejctn_F (fp2) -0.038 0.017 -2.253 0.024 -0.071 -0.005
## Rejection_F ~
## Growth_F (fa1) -0.689 0.377 -1.826 0.068 -1.428 0.051
## Growth_M (mp1) -0.783 0.360 -2.176 0.030 -1.489 -0.078
## Rejection_M ~
## Growth_M (ma1) -0.408 0.380 -1.075 0.282 -1.153 0.336
## Growth_F (fp1) -0.822 0.398 -2.064 0.039 -1.602 -0.041
## SxFrqn_M -1.610 0.527 -3.054 0.002 -2.643 -0.576
## Rejection_F ~
## SxFrqn_M -1.347 0.500 -2.696 0.007 -2.326 -0.368
## SexSatisfaction_M ~
## SxFrqn_M 0.361 0.081 4.479 0.000 0.203 0.519
## SexSatisfaction_F ~
## SxFrqn_M 0.462 0.093 4.960 0.000 0.280 0.645
## Std.lv Std.all
##
## -0.047 -0.229
## -0.034 -0.170
##
## -0.039 -0.225
## -0.038 -0.213
##
## -0.689 -0.204
## -0.783 -0.239
##
## -0.408 -0.121
## -0.822 -0.235
## -1.610 -0.281
##
## -1.347 -0.243
##
## 0.361 0.365
##
## 0.462 0.403
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Growth_F ~~
## Growth_M 1.383 0.266 5.191 0.000 0.861 1.905
## .Rejection_F ~~
## .Rejection_M 10.136 2.397 4.229 0.000 5.439 14.834
## .SexSatisfaction_F ~~
## .SexSatisfctn_M 0.405 0.073 5.554 0.000 0.262 0.547
## Growth_F ~~
## SexFrequency_M -0.269 0.138 -1.944 0.052 -0.540 0.002
## Growth_M ~~
## SexFrequency_M -0.110 0.140 -0.786 0.432 -0.386 0.165
## Std.lv Std.all
##
## 1.383 0.591
##
## 10.136 0.456
##
## 0.405 0.649
##
## -0.269 -0.194
##
## -0.110 -0.077
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .SexSatisfctn_F 0.721 0.100 7.211 0.000 0.525 0.916
## .SexSatisfctn_M 0.539 0.075 7.211 0.000 0.392 0.685
## .Rejection_F 21.078 2.923 7.211 0.000 15.349 26.808
## .Rejection_M 23.467 3.254 7.211 0.000 17.088 29.845
## Growth_F 2.268 0.315 7.211 0.000 1.651 2.884
## Growth_M 2.410 0.334 7.211 0.000 1.755 3.065
## SexFrequency_M 0.846 0.117 7.211 0.000 0.616 1.076
## Std.lv Std.all
## 0.721 0.649
## 0.539 0.653
## 21.078 0.813
## 23.467 0.848
## 2.268 1.000
## 2.410 1.000
## 0.846 1.000
##
## R-Square:
## Estimate
## SexSatisfctn_F 0.351
## SexSatisfctn_M 0.347
## Rejection_F 0.187
## Rejection_M 0.152
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ind1 0.033 0.022 1.459 0.145 -0.011 0.076
## ind2 0.016 0.016 0.978 0.328 -0.016 0.048
## ind3 0.026 0.018 1.419 0.156 -0.010 0.062
## ind4 0.032 0.021 1.553 0.120 -0.008 0.072
## ind5 0.037 0.023 1.620 0.105 -0.008 0.082
## Std.lv Std.all
## 0.033 0.047
## 0.016 0.027
## 0.026 0.043
## 0.032 0.053
## 0.037 0.055similar results have been reported in Cultice et al. (2022), page 1143:
“Next, we tested the model using the Actor-Partner Interdependence Model (APIM). As in Study 1, sex frequency was a predictor of sexual rejection sensitivity and sexual satisfaction. All exogenous variables were correlated. This model demonstrated good fit, \(\chi^2\) (4, \(N = 104\)) = 5.05, \(p = .28\), CFI = 1.0, TLI = .98, RMSEA = .05, SRMR = .03, AIC = 2703.79 (see Figure 3).
As in Study 1, partner growth mindset predicted one’s own sexual rejection sensitivity. Uniquely, in Study 2, perceived partner growth mindset was replaced with actual partner growth mindsets. For both men (\(\beta = -0.24, p = .04\)) and women (\(\beta = -0.24, p = .02\)), having a partner who had a greater sexual growth mindset predicted less sexual rejection sensitivity for oneself. For women, their own sexual rejection sensitivity was associated with lower sexual satisfaction for themselves (\(\beta = -0.23, p = .03\)), but men’s sexual rejection sensitivity was not a significant predictor of their own sexual satisfaction. For men and women, sexual frequency was associated with lower sexual rejection sensitivity for themselves and their partners and overall greater sexual satisfaction in both members of the couple.
Finally, no indirect effects were significant in Study 2. For women, neither the indirect paths from own sexual growth mindset, \(\beta = 0.05, p = .17\), 95% CI \([0.00, 0.14]\), nor partner’s sexual growth mindset, \(\beta = 0.06, p = .12\), 95% CI \([0.01, 0.15]\), to sexual satisfaction through rejection sensitivity were significant. The same pattern emerged for men: neither the indirect paths from own sexual growth mindset, \(\beta = 0.02, p = .41\), 95% CI \([-0.01, 0.10]\), nor partner’s sexual growth mindset, \(\beta = 0.04, p = .24\), 95% CI \([0.00, 0.14]\), to sexual satisfaction through rejection sensitivity were significant.”