# wp.sem.chisq: Statistical Power Analysis for Structural Equation Modeling... In WebPower: Basic and Advanced Statistical Power Analysis

 wp.sem.chisq R Documentation

## Statistical Power Analysis for Structural Equation Modeling based on Chi-Squared Test

### Description

Structural equation modeling (SEM) is a multivariate technique used to analyze relationships among observed and latent variables. It can be viewed as a combination of factor analysis and multivariate regression analysis. Two methods are widely used in power analysis for SEM. One is based on the likelihood ratio test proposed by Satorra and Saris (1985). The other is based on RMSEA proposed by MacCallum et al. (1996). This function is for SEM power analysis based on the likelihood ratio test.

### Usage

```wp.sem.chisq(n = NULL, df = NULL, effect = NULL, power = NULL,
alpha = 0.05)
```

### Arguments

 `n` Sample size. `df` Degrees of freedom. The degrees of freedom of the chi-squared test. `effect` Effect size. It specifies the population misfit of a SEM model, which is the difference between two SEM models: a full model (Mf) and a reduced model (Mr). A convienient way to get the effect size is to fit the reduced model using SEM software such R package 'lavaan' (Rossel, 2012). Then the effect size is calculated as the chi-squared statistics dividing by the sample size. `power` Statistical power. `alpha` significance level chosed for the test. It equals 0.05 by default.

### Value

An object of the power analysis.

### References

Satorra, A., & Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50(1), 83-90.

Rossel, Y. (2012). Lavaan: An R package for structural equation modeling and more. Version 0.5–12 (BETA). Retrieved from http://users. ugent. be/~ yrosseel/lavaan/lavaanIntroduction.

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

### Examples

```#To calculate the statistical power given sample size and effect size:
wp.sem.chisq(n = 100, df = 4, effect = 0.054, power = NULL, alpha = 0.05)
#    Power for SEM (Satorra & Saris, 1985)
#
#        n df effect     power alpha
#      100  4  0.054 0.4221152  0.05
#
#    URL: http://psychstat.org/semchisq

#To generate a power curve given a sequence of sample sizes:
res <- wp.sem.chisq(n = seq(100,600,100), df = 4,
effect = 0.054, power = NULL, alpha = 0.05)
res
#    Power for SEM (Satorra & Saris, 1985)
#
#        n df effect     power alpha
#      100  4  0.054 0.4221152  0.05
#      200  4  0.054 0.7510630  0.05
#      300  4  0.054 0.9145660  0.05
#      400  4  0.054 0.9750481  0.05
#      500  4  0.054 0.9935453  0.05
#      600  4  0.054 0.9984820  0.05
#
#    URL: http://psychstat.org/semchisq

#To plot the power curve:
plot(res)

#To generate a power curve given a sequence of alphas:
res <- wp.sem.chisq(n = 100, df = 4, effect = 0.054, power = NULL,
alpha = c(0.001, 0.005, 0.01, 0.025, 0.05))
res
#    Power for SEM (Satorra & Saris, 1985)
#
#        n df effect      power alpha
#      100  4  0.054 0.06539478 0.001
#      100  4  0.054 0.14952768 0.005
#      100  4  0.054 0.20867087 0.010
#      100  4  0.054 0.31584011 0.025
#      100  4  0.054 0.42211515 0.050
#
#    URL: http://psychstat.org/semchisq

#To calculate the required sample size given power and effect size:
wp.sem.chisq(n = NULL, df = 4, effect = 0.054, power = 0.8, alpha = 0.05)
#  Power for SEM (Satorra & Saris, 1985)
#
#           n df effect power alpha
#    222.0238  4  0.054   0.8  0.05
#
#  URL: http://psychstat.org/semchisq

#To calculate the minimum detectable effect size of one coefficent given power and sample size:
wp.sem.chisq(n = 100, df = 4, effect = NULL, power = 0.8, alpha = 0.05)
#    Power for SEM (Satorra & Saris, 1985)
#
#        n df    effect power alpha
#      100  4 0.1205597   0.8  0.05
#
#    URL: http://psychstat.org/semchisq
```

WebPower documentation built on May 21, 2022, 5:05 p.m.