# wp.blcsm: Statistical Power Curve for Bivariate Latent Change Score... In WebPower: Basic and Advanced Statistical Power Analysis

## Description

A longitudinal design often involves data collection on multiple variables from multiple participants at multiple times. Growth curve models (GCM) are structural equation models for longitudinal data analysis (McArdle & Epstein, 1987; McArdle & Nesselroade, 2014). Latent change score models (LCSM) combine difference equations with growth curves to investigate change in longitudinal studies . LCSM provied an efficient way to model nonlinear trajectory (e.g., McArdle, 2000; McArdle & Hamagami, 2001; Hamagami et al., 2010). This function is used to conduct power analysis for bivariate LCSMs based on a Monte Carlo method ( a method also used by Muth<c3><a9>n & Muth<c3><a9>n, 2002; Thoemmes et al., 2010; Zhang & Wang, 2009; Zhang, 2014). For each Monte Carlo replication, the Maximum likelihood ratio test is used for the model, while the Wald test is used for the parameter test. The method can obtain the power for testing each individual parameter of the models such as the change rate and coupling parameters.

## Usage

 ```1 2 3 4 5``` ```wp.blcsm(N = 100, T = 5, R = 1000, betay = 0, my0 = 0, mys = 0, varey = 1, vary0 = 1, varys = 1, vary0ys = 0, alpha = 0.05, betax = 0, mx0 = 0, mxs = 0, varex = 1, varx0 = 1, varxs = 1, varx0xs = 0, varx0y0 = 0, varx0ys = 0, vary0xs = 0, varxsys = 0, gammax = 0, gammay = 0, ...) ```

## Arguments

 `N` Sample size. It is 100 by default. `T` Number of measurement occasions. It is 5 by default. `R` Number of replications for the Monte Carlo simulation. It is 1000 by default. `betay` Parameter in the model: The compound rate of change for variable y. Its default value is 0. `my0` Parameter in the model: Mean of the initial latent score for variable y. Its default value is 0. `mys` Parameter in the model: Mean of the linear constant effect for variable y. Its default value is 0. `varey` Parameter in the model: Variance of the measurement error/uniqueness score for variable y. Its default value is 1. `vary0` Parameter in the model: Variance of the initial latent score for variable y. Its default value is 1. `varys` Parameter in the model: Variance of the linear constant effect for variable y. Its default value is 0. `vary0ys` Parameter in the model: Covariance of the initial latent score and the linear constant effect for variable y. Its default value is 0. `alpha` significance level chosed for the test. It equals 0.05 by default. `betax` Parameter in the model: The compound rate of change for variable x. Its default value is 0. `mx0` Parameter in the model: Mean of the initial latent score for variable x. Its default value is 0. `mxs` Parameter in the model: Mean of the linear constant effect for variable x. Its default value is 0. `varex` Parameter in the model: Variance of the measurement error/uniqueness score for variable x. Its default value is 1. `varx0` Parameter in the model: Variance of the initial latent score for variable x. Its default value is 1. `varxs` Parameter in the model: Variance of the linear constant effect for variable x. Its default value is 0. `varx0xs` Parameter in the model: Covariance of the initial latent score and the linear constant effect for variable x. Its default value is 0. `varx0y0` Parameter in the model: Covariance of the initial latent scores for y and x. Its default value is 0. `varx0ys` Parameter in the model: Covariance of the initial latent score for x and the linear constant effect for y. Its default value is 0. `vary0xs` Parameter in the model: Covariance of the initial latent score for y and the linear constant effect for x. Its default value is 0. `varxsys` Parameter in the model: Covariance of the linear constant effects for y and x. Its default value is 0. `gammax` Coupling parameter in the model: The effect of variable x on the change score of variable y. Its default value is 0. `gammay` Coupling parameter in the model: The effect of variable y on the change score of variable x. Its default value is 0. `...` Extra arguments. It is not required.

## Value

An object of the power analysis. The output of the R function includes 4 main pieces of information for each parameter in the model. The first is the Monte Carlo estimate (mc.est). It is calculated as the mean of the R sets of parameter estimates from the simulated data. Note that the Monte Carlo estimates should be close to the population parameter values used in the model. The second is the Monte Carlo standard deviation (mc.sd), which is calculated as the standard deviation of the R sets of parameter estimates. The third is the Monte Carlo standard error (mc.se), which is obtained as the average of the R sets of standard error estimates of the parameter estimates. Lastly, mc.power is the statistical power for each parameter.

## References

Zhang, Z., & Liu, H. (2018). Sample Size and Measurement Occasion Planning for Latent Change Score Models through Monte Carlo Simulation. In E. Ferrer, S. M. Boker, and K. J. Grimm (Eds.) Advances in Longitudinal Models for Multivariate Psychology: A Festschrift for Jack McArdle.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56``` ```## Not run: #To conduct power analysis for a bivariate LCSM with sample size equal to 100: wp.blcsm(N=100, T=5, R=1000, betay=0.08, my0=20, mys=1.5, varey=9, vary0=3, varys=1, vary0ys=0, alpha=0.05, betax=0.2, mx0=20, mxs=5, varex=9, varx0=3, varxs=1, varx0xs=0, varx0y0=1, varx0ys=0, vary0xs=0, varxsys=0, gammax=0, gammay=-.1) # pop.par mc.est mc.sd mc.se mc.power N T # betax 0.20 0.230 0.260 0.187 0.241 100 5 # betay 0.08 0.164 0.572 0.435 0.081 100 5 # gammax 0.00 -0.033 0.234 0.178 0.112 100 5 # gammay -0.10 -0.175 0.641 0.458 0.075 100 5 # mx0 20.00 20.004 0.336 0.326 1.000 100 5 # mxs 5.00 5.933 7.848 5.615 0.167 100 5 # my0 20.00 20.019 0.346 0.326 1.000 100 5 # mys 1.50 0.451 6.933 5.321 0.156 100 5 # varex 9.00 8.941 0.744 0.732 1.000 100 5 # varey 9.00 8.939 0.749 0.720 1.000 100 5 # varx0 3.00 3.029 1.243 1.222 0.739 100 5 # varx0xs 0.00 -0.210 0.768 0.767 0.030 100 5 # varx0y0 1.00 1.052 0.840 0.835 0.226 100 5 # varx0ys 0.00 -0.012 0.668 0.601 0.017 100 5 # varxs 0.60 2.343 6.805 2.687 0.090 100 5 # varxsys 0.00 0.072 3.559 1.740 0.019 100 5 # vary0 3.00 2.951 1.423 1.245 0.684 100 5 # vary0xs 0.00 0.198 2.263 1.629 0.031 100 5 # vary0ys 0.00 -0.371 1.970 1.511 0.106 100 5 # varys 0.05 1.415 3.730 2.096 0.024 100 5 #To conduct power analysis for a bivariate LCSM with sample size equal to 500: wp.blcsm(N=500, T=5, R=1000, betay=0.08, my0=20, mys=1.5, varey=9, vary0=3, varys=1, vary0ys=0, alpha=0.05, betax=0.2, mx0=20 , mxs=5, varex=9, varx0=3, varxs=1, varx0xs=0, varx0y0=1, varx0ys=0, vary0xs=0, varxsys=0, gammax=0, gammay=-.1) # pop.par mc.est mc.sd mc.se mc.power N T # betax 0.20 0.2009 0.031 0.031 1.000 500 5 # betay 0.08 0.0830 0.070 0.068 0.199 500 5 # gammax 0.00 -0.0014 0.030 0.029 0.057 500 5 # gammay -0.10 -0.1022 0.072 0.073 0.271 500 5 # mx0 20.00 19.9911 0.145 0.145 1.000 500 5 # mxs 5.00 5.0308 0.939 0.942 1.000 500 5 # my0 20.00 19.9999 0.143 0.146 1.000 500 5 # mys 1.50 1.4684 0.889 0.885 0.420 500 5 # varex 9.00 8.9836 0.340 0.328 1.000 500 5 # varey 9.00 8.9961 0.341 0.328 1.000 500 5 # varx0 3.00 3.0052 0.524 0.523 1.000 500 5 # varx0xs 0.00 -0.0144 0.222 0.230 0.047 500 5 # varx0y0 1.00 1.0064 0.360 0.360 0.808 500 5 # varx0ys 0.00 -0.0012 0.199 0.201 0.051 500 5 # varxs 1.00 1.0312 0.180 0.189 1.000 500 5 # varxsys 0.00 0.0028 0.161 0.163 0.045 500 5 # vary0 3.00 2.9777 0.519 0.547 1.000 500 5 # vary0xs 0.00 0.0072 0.286 0.294 0.035 500 5 # vary0ys 0.00 -0.0135 0.252 0.257 0.043 500 5 # varys 1.00 1.0246 0.260 0.253 0.999 500 5 ## End(Not run) ```

WebPower documentation built on May 1, 2019, 8:19 p.m.