Path analysis is an extension of the regression model, used to test the fit of the correlation matrix against two or more causal models which are being compared by the researcher. The model is usually depicted in a circle-and-arrow figure in which single-headed arrows indicate causation. A regression is calculated for each endogenous variable in the model as a dependent on others which the model indicates are causes. The standardized regression weights predicted by the model are the path coefficients. The covariance matrix implied by the model is compared with the observed covariance matrix for the variables and a goodness-of-fit statistic is calculated. The best-fitting of two or more models is selected by the researcher as the best model for advancement of theory.
Formerly path analysis was accomplished as a series of multiple linear regressions, one for each endogenous variable. This method yielded standardized regression coefficients (beta weights) and a R-square goodness of fit for each endogenous variable, but did not yield an overall goodness of fit for the model. Now path analysis is implemented by structural equation modeling (SEM) programs, which calculate all the paths simultaneously and yield an overall goodness of fit measure for the model. While SEM typically centers on latent variables, it is possible to model simple observed variables. When only observed variables are in the model, the researcher is conducting a path analysis.
In most software implementations, path analysis requires the usual assumptions of linear regression. It is particularly sensitive to model specification because failure to include relevant causal variables or inclusion of extraneous variables often substantially affects the path coefficients, which are used to assess the relative importance of various direct and indirect causal paths to the ultimate dependent variable. While it is possible to conduct path analysis on a single model, it is better if interpretations are based on comparing alternative models since goodness of fit is a relative concept which cannot prove that a single model is "correct".
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Below is the unformatted table of contents.
Table of Contents Overview 6 Key Concepts and Terms 7 Path model 7 Causal paths 7 Exogenous and endogenous variables 8 Path coefficient/path weight 8 Path coefficients 10 Path multiplication rule 10 Disturbance terms 11 Estimation 11 Effect decomposition 12 Example 1 13 Example 2 14 Path analysis through structural equation modeling 15 OLS path modeling vs. SEM path modeling 15 The SEM path model 15 Selecting outputs: The Analysis Properties dialog 16 Path estimates 17 Goodness of Fit measures 19 Correlations 21 Direct and indirect effects 21 Modification indexes 23 Assumptions 25 Linearity 25 Additivity 25 Interval level data 25 Uncorrelated error 25 Disturbance terms are uncorrelated with endogenous variables 25 Low multicollinearity 26 No underidentification or underdetermination of the model 26 Recursivity 26 Proper specification 26 Appropriate correlation input 27 Adequate sample size 27 The same sample 27 Frequently Asked Questions 28 Does path analysis confirm causation in a model? 28 Can path analysis be used for exploratory rather than confirmatory purposes? 28 How do I know if my model is "underidentified" and what difference does it make? How does this relate to "recursivity? 29 How does the significance of a path coefficient compare with the significance of the corresponding regression coefficient? 29 How do you assess the significance of the total (direct and indirect) effect of exogenous variable x on endogenous variable y? 29 Why might the direct effect be zero? 29 How are path coefficients related to the correlation matrix for purposes of testing a model? 29 How, exactly, can I compute path coefficients in SPSS? 31 How do I compute the value of the path from an error term to an endogenous variable? 32 How can multiple group path analysis determine if the path model differs across groups in my sample? 32 Could I substitute logistic regression when doing effect decomposition? 32 Can path analysis handle hierarchical/multilevel data? 32 Are regression and SEM the only approaches to path analysis? 33 Bibliography 33