Path Analysis using lm and lavaan

Transcription

1 Path Analysis using lm and lavaan Grant B. Morgan Baylor University September 10, 2014 First of all, this post is going to mirror a page on the Institute for Digital Research and Education (IDRE) site that demonstrates how to conduct path analysis using SAS. If you haven t discovered the IDRE site already, you really should check it out because it s fantastic! I have visited their Statistics site countless times for help with SAS, R, Mplus, and L A TEXcode over the years. You can find it at The page I will replicate using R can be found at I will use the HSB dataset, which is at the time of this post publicly available on the IDRE site. The file is in sas7bdat format so we ll first need to get the data into R and then we ll ready to go. Import the data into R from SAS format Fortunately, there is a package that reads sas7bdat files into *R* so I ll use that. library(sas7bdat) path.data<-read.sas7bdat(" head(path.data) id female race ses schtyp prog read write math science socst The Model The model that we re going to be estimating is below. 1

2 We need to provide estimates for each of the parameters in the model. Old School Path Analysis In the old(er) days, we would need to estimate the model in a few different parts. First, we d need to estimate the correlation between reading and writing scores. Then, we d need to estimate a model for each endogenous variable separately. Let s go through these steps below. Step 1: Estimate the correlation between reading and writing scores. cor(path.data$read, path.data$write) [1] Step 2a: Estimate the model predicting math scores. Let s estimate the math model first. math.model<-lm(math~read+write, data=path.data) Now we need to get the standardized coefficients. The easiest way to do this is with the lm.beta function in the QuantPsyc package. library(quantpsyc) lm.beta(math.model) read write

3 Step 2b: Estimate the model predicting science scores. Let s estimate the science model first. science.model<-lm(science~read+write+math, data=path.data) Now we need to get the standardized coefficients. lm.beta(science.model) read write math Step 3a: Calculate the errors of the endogenous variables. We ve gotten all of the path coefficients so last, let s get those pesky error terms. It s been a while since I did this from memory, but this feels right. The error for the math model can be computed using e m = 1 R 2 m, and the error for the science model can be computed using e s = 1 R 2 s. # Math error sqrt(1-summary(math.model)$r.squared) [1] # Science error sqrt(1-summary(science.model)$r.squared) [1] Step 4: Fill in values for the appropriate estimate. That s the old school way of conduct path analysis. New School Path Analysis Path analysis is much easier by adopting a structural equation modeling framework, which allows us to specify which relationships and paths we want and then estimate the model in one step. There are a few packages in R that we could use, but I tend to use the lavaan package for these sorts of analysis. Let s get to it. Step 1: Specify the model. 3

4 library(lavaan) path.model<-' math ~ read + write science ~ read + write + math read~~write math~~math science~~science ' Step 2: Estimate the model. path.fitted<-sem(path.model, data=path.data, fixed.x=false) summary(path.fitted, standardized=true) lavaan (0.5-16) converged normally after 33 iterations Number of observations 200 Estimator ML Minimum Function Test Statistic Degrees of freedom 0 P-value (Chi-square) Parameter estimates: Information Expected Standard Errors Standard Estimate Std.err Z-value P(> z ) Std.lv Std.all Regressions: math ~ read write science ~ read write math Covariances: read ~~ write Variances: math

5 science read write The estimates that we want are in the columns labeled Std.all. If we want this model to match what we did previously, we simply need to take the square root of the residual variances to get the same errors as before. For the math error, (.485) =.696. For the science error, (.500) =.707. That s is. Path analysis = Done. 5