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Enjoy this brief demonstration of the fit observed data module (i.e., a simple mediation model).
Also, please see Fit Latent Data.
# Number of observations
n <- 1000
# Coefficient for a path (x -> m)
a <- .75
# Coefficient for b path (m -> y)
b <- .80
# Coefficient for total effect (x -> y)
c <- .60
# Coefficient for indirect effect (x -> m -> y)
ab <- a * b
# Coefficient for direct effect (x -> y)
cd <- c - ab
# Compute x, m, y values
set.seed(100)
x <- rnorm(n)
m <- a * x + sqrt(1 - a^2) * rnorm(n)
eps <- 1 - (cd^2 + b^2 + 2*a * cd * b)
y <- cd * x + b * m + eps * rnorm(n)
data <- data.frame(y = y,
x = x,
m = m)set.seed(102)
## create 5 y variables, 5 x variables and 5 m variables with jittered data
jitter.data <- lapply(1:5, function (i) {
apply(data , 2 , function (x) jitter(x , amount=1))
})
# Create data frame with jittered observed variables
jitter.data <- data.frame( sapply(jitter.data, "[" ,,1) , # First column (y)
sapply(jitter.data, "[" ,,2) , # Second column (x)
sapply(jitter.data, "[" ,,3) # Third column (m)
)
# Add column names
colnames(jitter.data) <- c( paste0("y",1:5) , paste0("x",1:5) , paste0("m",1:5))model <- '
y =~ y1+y2+y3+y4+y5
x =~ x1+x2+x3+x4+x5
m =~ m1+m2+m3+m4+m5
# direct effect
y ~ c*x
# mediator
m ~ a*x
y ~ b*m
# indirect effect (a*b)
ab := a*b
# total effect
cd := c + (a*b)
'
jitter.fit <- lavaan::sem(model, data = jitter.data)
lavaan::summary(jitter.fit)
#> lavaan 0.6-10 ended normally after 34 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 33
#>
#> Number of observations 1000
#>
#> Model Test User Model:
#>
#> Test statistic 53.272
#> Degrees of freedom 87
#> P-value (Chi-square) 0.998
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> y =~
#> y1 1.000
#> y2 0.998 0.030 33.055 0.000
#> y3 0.993 0.030 33.196 0.000
#> y4 0.940 0.030 31.517 0.000
#> y5 1.015 0.030 33.374 0.000
#> x =~
#> x1 1.000
#> x2 1.013 0.026 39.481 0.000
#> x3 0.986 0.026 38.610 0.000
#> x4 0.993 0.026 38.412 0.000
#> x5 0.983 0.026 38.157 0.000
#> m =~
#> m1 1.000
#> m2 0.963 0.026 37.703 0.000
#> m3 0.975 0.026 38.157 0.000
#> m4 1.009 0.026 38.710 0.000
#> m5 0.970 0.025 38.053 0.000
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> y ~
#> x (c) -0.014 0.029 -0.466 0.641
#> m ~
#> x (a) 0.791 0.030 26.756 0.000
#> y ~
#> m (b) 0.758 0.035 21.965 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .y1 0.303 0.016 18.350 0.000
#> .y2 0.330 0.018 18.705 0.000
#> .y3 0.321 0.017 18.641 0.000
#> .y4 0.351 0.018 19.322 0.000
#> .y5 0.328 0.018 18.558 0.000
#> .x1 0.304 0.017 17.798 0.000
#> .x2 0.318 0.018 17.879 0.000
#> .x3 0.329 0.018 18.276 0.000
#> .x4 0.341 0.019 18.360 0.000
#> .x5 0.343 0.019 18.464 0.000
#> .m1 0.351 0.019 18.848 0.000
#> .m2 0.329 0.017 18.884 0.000
#> .m3 0.321 0.017 18.704 0.000
#> .m4 0.322 0.017 18.468 0.000
#> .m5 0.321 0.017 18.746 0.000
#> .y 0.165 0.014 12.069 0.000
#> x 1.048 0.060 17.520 0.000
#> .m 0.420 0.028 15.216 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.599 0.032 18.475 0.000
#> cd 0.586 0.027 22.025 0.000bayesian.jitter.fit <- bfw(project.data = jitter.data,
observed = "x1,x2,x3,x4,x5,
m1,m2,m3,m4,m5,
y1,y2,y3,y4,y5",
latent.names = "Independent,Mediator,Dependent",
additional = "indirect <- xm * my , total <- xy + (xm * my)",
additional.names = "AB,C",
jags.model = "fit",
jags.seed = 102,
silent = TRUE)
round(bayesian.jitter.fit$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> lam[1]: X1 0.999 0 1.000 1.000 1000
#> lam[2]: X2 1.019 1309 0.966 1.067 1000
#> lam[3]: X3 0.988 1420 0.941 1.042 1000
#> lam[4]: X4 0.998 1440 0.946 1.048 1000
#> lam[5]: X5 0.990 1402 0.932 1.035 1000
#> lam[6]: M1 0.999 0 1.000 1.000 1000
#> lam[7]: M2 0.964 1164 0.912 1.013 1000
#> lam[8]: M3 0.970 1049 0.927 1.026 1000
#> lam[9]: M4 1.013 1075 0.959 1.062 1000
#> lam[10]: M5 0.969 1117 0.921 1.022 1000
#> lam[11]: Y1 0.999 0 1.000 1.000 1000
#> lam[12]: Y2 1.004 1136 0.939 1.059 1000
#> lam[13]: Y3 0.994 1139 0.933 1.050 1000
#> lam[14]: Y4 0.941 1270 0.883 0.999 1000
#> lam[15]: Y5 1.023 1149 0.954 1.074 1000
#> error[1]: X1 0.304 4691 0.273 0.340 1000
#> error[2]: X2 0.321 4464 0.285 0.355 1000
#> error[3]: X3 0.327 4637 0.296 0.366 1000
#> error[4]: X4 0.343 5200 0.305 0.379 1000
#> error[5]: X5 0.346 4795 0.309 0.383 1000
#> error[6]: M1 0.352 5155 0.315 0.388 1000
#> error[7]: M2 0.329 5256 0.296 0.365 1000
#> error[8]: M3 0.319 4979 0.288 0.355 1000
#> error[9]: M4 0.321 4903 0.291 0.358 1000
#> error[10]: M5 0.322 5080 0.288 0.356 1000
#> error[11]: Y1 0.300 4509 0.272 0.337 1000
#> error[12]: Y2 0.333 4645 0.298 0.367 1000
#> error[13]: Y3 0.317 5032 0.288 0.356 1000
#> error[14]: Y4 0.350 5481 0.317 0.388 1000
#> error[15]: Y5 0.329 4929 0.294 0.364 1000
#> cov[1,1]: Independent vs. Independent 1.044 884 0.968 1.114 1000
#> cov[2,1]: Mediator vs. Independent 0.822 949 0.781 0.872 1000
#> cov[3,1]: Dependent vs. Independent 0.609 936 0.574 0.647 1000
#> cov[1,2]: Independent vs. Mediator 0.822 949 0.781 0.872 1000
#> cov[2,2]: Mediator vs. Mediator 1.071 669 0.994 1.151 1000
#> cov[3,2]: Dependent vs. Mediator 0.798 776 0.756 0.848 1000
#> cov[1,3]: Independent vs. Dependent 0.609 936 0.574 0.647 1000
#> cov[2,3]: Mediator vs. Dependent 0.798 776 0.756 0.848 1000
#> cov[3,3]: Dependent vs. Dependent 0.759 683 0.701 0.827 1000
#> beta[2,1]: Mediator vs. Independent 0.788 1308 0.735 0.850 1000
#> beta[3,1]: Dependent vs. Independent -0.014 1008 -0.072 0.043 1000
#> beta[3,2]: Dependent vs. Mediator 0.760 630 0.696 0.828 1000
#> indirect[1]: AB 0.593 917 0.535 0.662 1000
#> total[1]: C 0.587 1713 0.534 0.640 1000
#> Fit (Predicted) 80.578 5928 69.388 97.268 1000
#> Fit (Simulated) 119.033 10000 92.518 152.408 1000
#> Fit (Discrepancy) -38.274 9228 -71.546 -5.316 1000
#> PPP 0.991 20 0.988 0.992 1000biased.sigma <-matrix(c(1,1,0,1,1,0,0,0,1),3,3)
set.seed(101)
noise <- MASS::mvrnorm(n=2,
mu=c(200, 300, 0),
Sigma=biased.sigma,
empirical=FALSE)
colnames(noise) <- c("y","x","m")
biased.data <- rbind(data,noise)
jitter.noise <- noise[,rep(1:3,each=5)]
colnames(jitter.noise) <- c( paste0("y",1:5) , paste0("x",1:5) , paste0("m",1:5))
biased.jitter.data <- rbind(jitter.data, jitter.noise)biased.jitter.fit <- lavaan::sem(model, data = biased.jitter.data)
lavaan::summary(biased.jitter.fit)
#> lavaan 0.6-10 ended normally after 254 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 33
#>
#> Number of observations 1002
#>
#> Model Test User Model:
#>
#> Test statistic 53.395
#> Degrees of freedom 87
#> P-value (Chi-square) 0.998
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> y =~
#> y1 1.000
#> y2 1.000 0.003 356.708 0.000
#> y3 1.000 0.003 358.478 0.000
#> y4 0.999 0.003 352.757 0.000
#> y5 1.000 0.003 358.036 0.000
#> x =~
#> x1 1.000
#> x2 1.000 0.002 538.595 0.000
#> x3 1.000 0.002 535.008 0.000
#> x4 1.000 0.002 529.637 0.000
#> x5 1.000 0.002 530.683 0.000
#> m =~
#> m1 1.000
#> m2 0.967 0.026 37.620 0.000
#> m3 0.972 0.026 37.466 0.000
#> m4 1.010 0.026 38.362 0.000
#> m5 0.967 0.026 37.414 0.000
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> y ~
#> x (c) 0.666 0.002 319.095 0.000
#> m ~
#> x (a) 0.004 0.003 1.501 0.133
#> y ~
#> m (b) 0.229 0.021 10.733 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .y1 0.301 0.017 18.170 0.000
#> .y2 0.332 0.018 18.564 0.000
#> .y3 0.326 0.018 18.490 0.000
#> .y4 0.346 0.018 18.724 0.000
#> .y5 0.328 0.018 18.509 0.000
#> .x1 0.303 0.017 17.775 0.000
#> .x2 0.320 0.018 18.032 0.000
#> .x3 0.329 0.018 18.144 0.000
#> .x4 0.341 0.019 18.307 0.000
#> .x5 0.339 0.019 18.276 0.000
#> .m1 0.349 0.019 17.965 0.000
#> .m2 0.319 0.018 17.852 0.000
#> .m3 0.327 0.018 17.932 0.000
#> .m4 0.319 0.018 17.435 0.000
#> .m5 0.326 0.018 17.959 0.000
#> .y 0.348 0.020 17.389 0.000
#> x 180.449 8.075 22.346 0.000
#> .m 1.072 0.063 17.123 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.001 0.001 1.488 0.137
#> cd 0.666 0.002 309.325 0.000bayesian.biased.jitter.fit <- bfw(project.data = biased.jitter.data,
observed = "x1,x2,x3,x4,x5,
m1,m2,m3,m4,m5,
y1,y2,y3,y4,y5",
latent.names = "Independent,Mediator,Dependent",
additional = "indirect <- xm * my , total <- xy + (xm * my)",
additional.names = "AB,C",
jags.model = "fit",
run.robust = TRUE,
jags.seed = 103,
silent = TRUE)
round(bayesian.biased.jitter.fit$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> lam[1]: X1 0.999 0 1.000 1.000 1002
#> lam[2]: X2 1.011 813 0.961 1.068 1002
#> lam[3]: X3 0.983 846 0.933 1.037 1002
#> lam[4]: X4 0.987 833 0.938 1.048 1002
#> lam[5]: X5 0.973 906 0.925 1.032 1002
#> lam[6]: M1 0.999 0 1.000 1.000 1002
#> lam[7]: M2 0.961 633 0.911 1.014 1002
#> lam[8]: M3 0.977 624 0.925 1.026 1002
#> lam[9]: M4 1.014 588 0.958 1.060 1002
#> lam[10]: M5 0.969 630 0.921 1.022 1002
#> lam[11]: Y1 0.999 0 1.000 1.000 1002
#> lam[12]: Y2 0.998 765 0.940 1.062 1002
#> lam[13]: Y3 1.012 816 0.943 1.068 1002
#> lam[14]: Y4 0.938 936 0.876 0.999 1002
#> lam[15]: Y5 1.023 717 0.962 1.090 1002
#> error[1]: X1 0.223 1986 0.186 0.255 1002
#> error[2]: X2 0.230 2228 0.200 0.275 1002
#> error[3]: X3 0.249 2177 0.214 0.287 1002
#> error[4]: X4 0.263 2074 0.223 0.299 1002
#> error[5]: X5 0.271 2583 0.232 0.308 1002
#> error[6]: M1 0.343 3209 0.309 0.381 1002
#> error[7]: M2 0.324 2957 0.289 0.359 1002
#> error[8]: M3 0.312 2928 0.282 0.352 1002
#> error[9]: M4 0.315 2939 0.283 0.352 1002
#> error[10]: M5 0.319 3258 0.284 0.352 1002
#> error[11]: Y1 0.221 2172 0.192 0.260 1002
#> error[12]: Y2 0.259 2553 0.226 0.297 1002
#> error[13]: Y3 0.248 2543 0.209 0.279 1002
#> error[14]: Y4 0.284 2934 0.247 0.322 1002
#> error[15]: Y5 0.250 2396 0.215 0.288 1002
#> cov[1,1]: Independent vs. Independent 1.051 543 0.974 1.126 1002
#> cov[2,1]: Mediator vs. Independent 0.825 597 0.782 0.872 1002
#> cov[3,1]: Dependent vs. Independent 0.604 603 0.566 0.643 1002
#> cov[1,2]: Independent vs. Mediator 0.825 597 0.782 0.872 1002
#> cov[2,2]: Mediator vs. Mediator 1.070 377 0.997 1.159 1002
#> cov[3,2]: Dependent vs. Mediator 0.797 541 0.746 0.838 1002
#> cov[1,3]: Independent vs. Dependent 0.604 603 0.566 0.643 1002
#> cov[2,3]: Mediator vs. Dependent 0.797 541 0.746 0.838 1002
#> cov[3,3]: Dependent vs. Dependent 0.761 458 0.701 0.832 1002
#> beta[2,1]: Mediator vs. Independent 0.787 715 0.732 0.847 1002
#> beta[3,1]: Dependent vs. Independent -0.024 621 -0.080 0.041 1002
#> beta[3,2]: Dependent vs. Mediator 0.750 420 0.684 0.825 1002
#> indirect[1]: AB 0.588 604 0.528 0.660 1002
#> total[1]: C 0.572 1358 0.523 0.629 1002These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.