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manual:diagram_based_power_analysis

# Conduct Monte Carlo based power analysis using the path diagram interface

Once can conduct power analysis using Monte Carlo based method by drawing a path diagram with population parameters. An example is given in the figure below:

## Rules to draw the path diagram

### Shapes

• : Observed variables.
• : Latent variables / factors
• : Mean / intercept
• : Skewness/kurtosis
• : Missing data
• : Double-headed arrows for variances / covariances

### Rules

• Click or or to draw the shape directly.
• To draw , first select one of the above three shapes and then click the button on the left panel.
• To draw , first select or , and then click button on the left panel.
• To draw paths between two shapes
• Method 1: Click or , then drag your mouse from the start variable to the end variable while pressing the left button of your mouse.
• Method 2: Click the start variable, then click the arrow path, and then the end variable.
• Adjust the diagram. Click any shape to highlight it, then move it around.
• Copy the diagram. First select the shapes by clicking the shapes while holding the “Ctrl” key on your keyboard. Then, click the button to paste.
• While holing the “Ctrl” key, one can drag a selection window by pressing the right button of the mouse to select multiple shapes.

## Rules to specify the population parameters

• A number such as 1, 0.5, and -2, on the path will be used as population parameters to generate data from the model and the path will be estimated as free parameters in Monte Carlo simulation.
• To fix a path in the estimation, use @. For example, @1 will be fixed at 1.
• A path can be provided a name.
• For example, a?0.5 means the parameter values is 0.5, the parameter name is a, and the path needs to be estimated.
• a@0.5 means the parameter values is 0.5, the parameter name is a, and the path will be fixed at 0.5 when estimating the model.
• To specify the skewness and kurtosis for an observed variables, using the path from to . Two numbers separated by “;” are used with first one denoting the skewness and the second one denoting the kurtosis.
• Default parameters
• By default, the unspecified variances will be given the value 1 and the unspecified covariance will be given the value 0.
• The unspecified mean/intercept will be givens a value 0.

## Conduct the power analysis

### Required input

• Sample size: an integer number for sample size
• Significance level: 0.05 typically
• MC replications: How many Monte Carlo replications are used to estimate power. 1000 typically.
• Power parameters: Parameters other than specified in the diagram. For example, one can get the power for an indirect effect a*b. To get it, specify ab := a*b. Notice that “:=” is used to define a new parameter. Each line provides one such parameter.
• Notes: put a note for the analysis.

### Required input

• To save the current path diagram, click the button
• To open an older path diagram, click the button
• To run the power analysis, click the button
• To see the output of the power analysis, click the button
• To download the path diagram as a SVG figure, click the button
• To draw a new path diagram, click the button