The 3 Different Sum of Squares

You may have noticed that your software output specified a *Type __* Sum of Squares. This tutorial will explain what that means, and the differences between Type I, Type II, and Type III sum of squares using two-way factorial ANOVA as an example. It can be shown that the \(F\) test for a one-way ANOVA is equivalent to comparing the full model to a reduced model. This is equivalent to asking if we are able to improve our prediction of the outcome by including the variable in the model, or if our guesses are just as noisy with the variable as without.
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Two-Way ANOVA

This tutorial is going to take what we learned in one-way ANOVA and extend it to two-way ANOVA. In a one-way ANOVA, we have A single dependent variable measured on an interval scale A single independent variable measured on a nominal scale The example used in our one-way ANOVA tutorial was the cook times of four different brands of pasta. The brand of pasta was the independent variable, and the cook time (in minutes) was the dependent variable.
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CFA using the lavaan package in R

This tutorial shows how to estimate a confirmatory factor analysis (CFA) model using the R lavaan package. The model, which consists of two latent variables and eight manifest variables, is described here. To review, the model to be fit is the following: The data can be accessed from the built-in Bollen dataset in the sem package. library(sem) ## Warning: package 'sem' was built under R version 3.6.3 library(lavaan) data("Bollen") All required packages are loaded first with the library() commands.
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SEM using the lavaan package in R

This tutorial shows how to estimate a full structural equation model (SEM) with latent variables using the lavaan package in R. The model consists of three latent variables and eleven manifest variables, as described here. To review, the model to be fit is the following: The data can be accessed from the built-in Bollen dataset in the sem package. library(sem) ## Warning: package 'sem' was built under R version 3.6.3 library(lavaan) data("Bollen") All required packages are loaded first with the library() commands.
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SEM in Mplus

This page describes how to set up code in Mplus to fit a full structural equation model with latent variables. The model consists of three latent variables and eleven manifest variables, as described here. Mplus only reads data in text format, see this post for details on how to prepare a data file for Mplus. The data can be accessed from Github. To review, the model to be fit is the following:
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CFA in Mplus

This page describes how to set up code in Mplus to fit a confirmatory factor analysis (CFA) model. The model, which consists of two latent variables and eight manifest variables, is described here. Mplus only reads data in text format, see this post for details on how to prepare a data file for Mplus. The data can be accessed from Github. To review, the model to be fit is the following:
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A Running CFA and SEM Example

Industrialization and Democracy (Bollen, 1989) The CFA and SEM examples are taken from data analyzed in Kenneth Bollen’s (1989) book Structural Equations with Latent Variables. The goal of the model is to determine how democracy and industrialization in 1960 are associated with democracy in 1965. The problem is that there are no good single items that capture the entirety of the concepts of democracy and industrialization. Hence, these concepts are treated as latent (unobserved) variables imperfectly measured by a set of observed indicators.
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Preparing Data for Mplus

From SPSS Mplus requires data to be read in from a text file without variable names, with numeric values only, and with missing data coded as a single numeric value, such as -999. A common workflow for preparing data to analyze in Mplus is to perform the variable cleaning in SPSS and then save the data as a text file. This guide shows the appropriate steps using the sample file bollen_sem.
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How Can I Read Data Into R?

To read and write Excel files from R, click here. To read and write SPSS, SAS and Stata files from R, click here. To read and write text files from R, click here.

Reading and Writing Excel Files With R Using readxl and writexl

This tutorial walks you through how to use the readxl package to read Microsoft Excel .xls and .xlsx file formats into R, and how to export data from R back out to an Excel format using the writexl package. readxl’s functions are related to importing Excel files into a tibble object, which is modern R’s internal data format. A tibble can then be manipulated to create summary tables or plots, run statistical tests, or perform other common analysis tasks.
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