I have a huge problem right now and I will be grateful if you guys could help me in this regard. Roughly, my study is regarding modeling seahorse extract on asthma by using Structural Equation Modeling (SEM) and in order to minimize the residual in model, I will use bootstrapping method (by using R language). My first question is:
My problem is I got confused which model to use between these two:
i) Multiple linear regression (Yi=β0+ β1X1i+ β2X2i +ei) or
ii) Covariance algebra model COV(Y1,Y2)=COV(γ11X1+ε1, β21Y1+ γ21X1+ε1)
For the 2nd model, I referred to the book Using Multivariate Statistics written by Barbara G.Tabachnick & Linda S.Fidell (1996), Chapter 14 written by Prof. Dr Ullman on the page 717. This book was published by Harper Collins College Publishers.
Second question is what is the difference between basic multiple linear regression and multiple linear regression that we have in SEM? It would be my pleasure if you could help me solve this matter.
Thank you.
Have a good day.
"It is unclear what you are asking" (one of the standard pre-coded replies on CrossValidated, stats.stackexchange.com).
Bootstrapping does not minimize residuals; it is a method to construct standard errors or confidence intervals, and with some extra tricks, produce tests. (People in data mining/machine learning also use bootstrap aggregation to quantify performance of their classifiers out of sample, but we are talking about SEM here, I guess). Please explain what it is exactly that you are doing with the bootstrap.
The two equations you gave are incomparable. The first one uses Y, X1 and X2, while the second one uses Y1, Y2 and X1. They serve different purposes. Please edit your question and clarify.
On your second question, Pat is right: there is no difference. However, using SEM packages to fit a multiple regression model as a saturated SEM model is akin to using microscopes to hammer nails into woodboard. The standard packages like R, Stata or SAS would have diagnostic tools in their regression modules for residual, influence and nonlinearity diagnostics (such as say plot( fitted(model), residuals(model) ) which won't be feasible with SEM. While Pat is also right that the standard regression packages do not deal with missing data in predictors particularly well, the SEM packages would have to make some silly assumptions like multivariate normality of the explanatory variables (and I am yet to see a data set of sufficient size where that assumption is justified). For the missing data in predictors problem, I would utilize a multiple imputation approach with careful review of what it is that I am imputing (http://ideas.repec.org/a/tsj/stataj/v12y2012i3p353-367.html).
I'll take the second question:
If you are using path analysis for your SEM (manifest variables in structural equation modeling software, not full SEM with measurement modeling) and a saturated model, they are essentially identical. In most cases, the only difference will be if you have missing data, as better missing data handling is incorporated in typical SEM software than in typical linear regression software.
Pat
"It is unclear what you are asking" (one of the standard pre-coded replies on CrossValidated, stats.stackexchange.com).
Bootstrapping does not minimize residuals; it is a method to construct standard errors or confidence intervals, and with some extra tricks, produce tests. (People in data mining/machine learning also use bootstrap aggregation to quantify performance of their classifiers out of sample, but we are talking about SEM here, I guess). Please explain what it is exactly that you are doing with the bootstrap.
The two equations you gave are incomparable. The first one uses Y, X1 and X2, while the second one uses Y1, Y2 and X1. They serve different purposes. Please edit your question and clarify.
On your second question, Pat is right: there is no difference. However, using SEM packages to fit a multiple regression model as a saturated SEM model is akin to using microscopes to hammer nails into woodboard. The standard packages like R, Stata or SAS would have diagnostic tools in their regression modules for residual, influence and nonlinearity diagnostics (such as say plot( fitted(model), residuals(model) ) which won't be feasible with SEM. While Pat is also right that the standard regression packages do not deal with missing data in predictors particularly well, the SEM packages would have to make some silly assumptions like multivariate normality of the explanatory variables (and I am yet to see a data set of sufficient size where that assumption is justified). For the missing data in predictors problem, I would utilize a multiple imputation approach with careful review of what it is that I am imputing (http://ideas.repec.org/a/tsj/stataj/v12y2012i3p353-367.html).
The SEM modeling combines the confirmatory factor analysis and the multiple regression analysis (simultaneous equations models) into the comprehensive modeling framework.
Hi. Firstly, thank you so much for your answers. I am really grateful for your quick feedback. I’m so sorry because it took me so long to reply your comments. Last week was my crazy week.Okay, let me clear my question.
My research is about modeling seahorse extract on asthma by using Structural Equation Modeling (SEM). I will be using statistical software AMOS for conducting Confirmatory Factor Analysis and SEM. After my hypothesized model fit with data (all fitness indexes were achieved), I wish to use bootstrap procedure to estimate the standard error of the parameter estimate and create the confidence intervals in SEM by using software R language.
So, my problem is I don’t know what model should I put as coding in R? In other words, what model/equation should I use to estimate the standard error in SEM?
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