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# 7.3 Monte Carlo Simulation for Sample Size Estimation

Monte Carlo methods are computerized mathematical techniques that use random sampling and computer simulation to solve problems. The term ‘Monte Carlo methods’ was coined by physicists working on nuclear weapon projects in the 1940s who named it for the city in Monaco famed for its casino and games of chance. Monte Carlo simulation has been increasingly used for power analysis in SEM, and computer software like Mplus provides a user-friendly approach for such a simulation.

To apply Monte Carlo simulation to estimate power and sample size for a desired SEM model, a hypothesized population value for each parameter of the model needs to be specified either based on the best theoretical guess or the empirical finding. Based on the population values of the model parameters, a large number of samples (replications) are randomly generated, and the same model is estimated for each of the samples/replications. As such, the estimates of each parameter from all the replications form a distribution of the parameter estimates, enabling the behavior of the parameter estimates to be checked. From the results of Monte Carlo simulation one can not only examine parameter estimate precision, but also determine the sample size needed to ensure large enough statistical power (e.g., ≥80). In this section, we demonstrate how to use Monte Carlo simulation to estimate adequate sample size for a CFA model and a LGW model with a detailed description of ...

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