Path Analysis Explained: Meaning, Diagram, R, SPSS and a Free Online Tool
Path analysis (also called path analysis in statistics) tests a causal story among observed variables with a set of regressions and splits each relationship into direct, indirect and total effects. This guide covers the path analysis meaning, the path analysis diagram, path analysis vs SEM, how to run it in R and SPSS, and an example from plant breeding, with the original studies linked so you can read the sources.
Path analysis meaning and origin
Path analysis was introduced by the geneticist Sewall Wright, first applied to inheritance data and set out in Wright (1934), The method of path coefficients after his earlier paper, Wright (1921), Correlation and causation. Plant scientists adopted it in the late 1950s: Dewey and Lu (1959) used path coefficients to analyse components of crested wheatgrass seed production, and Li (1956) described the concept and its impact on population genetics. A path model cannot prove causation. It shows whether your data are consistent with the causal structure you specified.
Direct, indirect and total effects
If X affects M with β = 0.50 and M affects Y with β = 0.40, the indirect effect of X on Y through M is 0.50 × 0.40 = 0.20. Add the direct X → Y path (say 0.20) and the total effect is 0.40. Bootstrap confidence intervals are the recommended way to test indirect effects, as discussed in Preacher and Hayes (2008).
Path analysis diagram
A path analysis diagram uses rectangles for observed variables, single-headed arrows for directed effects and curved double-headed arrows for correlations. Arrow labels show the coefficients, and dashed arrows mark non-significant paths. The StatFas calculator draws the diagram for you and exports SVG or 300 dpi PNG, which also works well as the main slide in a path analysis PPT.
Path analysis vs SEM
Path analysis uses only observed variables and assumes they are measured without error. Structural equation modeling (SEM) adds latent variables and a measurement model. Path analysis is therefore a special case of SEM. Use the SEM calculator when your constructs are measured by several items, and the mediation calculator for a single mediator.
Path analysis in R
library(lavaan)
model <- 'M ~ a*X
Y ~ b*M + c*X
indirect := a*b
total := c + a*b'
fit <- sem(model, data = df, se = "bootstrap", bootstrap = 5000)
summary(fit, standardized = TRUE, fit.measures = TRUE)The lavaan package is described in Rosseel (2012). Read the standardized estimates and the interval for indirect; if it excludes zero, the indirect path is supported.
Path analysis in SPSS
Base SPSS has no path module. Run one regression per endogenous variable and use the standardized Beta values as path coefficients, or use IBM SPSS Amos for fit indices and a drawn diagram. The PROCESS macro covers simple mediation with bootstrapping.
Path analysis in plant breeding
Breeders use path analysis to separate the correlation between a yield component and grain yield into a direct effect and indirect effects through other traits, following Dewey and Lu (1959). Take grain yield as the outcome and plant height, number of tillers, spike length, grain weight and biological yield as correlated causes. For trait i, the correlation with yield equals its direct effect plus the sum over other traits j of rij × pjy. A trait with a strong correlation but a small direct effect mostly travels with another trait, so selecting on it alone is less effective. Also report the residual effect, √(1 − R²), and check multicollinearity.
Interpretation, fit and APA 7 reporting
A standardized path coefficient is the SD change in the outcome for a one-SD change in the predictor, holding the other predictors constant. For over-identified models, report χ²(df), CFI, TLI, RMSEA and SRMR. The cutoffs in Hu and Bentler (1999) are guidelines, not strict rules. Sample size has no single rule; common guidance is at least 10 to 20 cases per estimated parameter. In APA 7, report the estimator, N, the model, fit, coefficients with intervals, the bootstrap details and the diagram.
References
- Wright, S. (1921). Correlation and causation. Journal of Agricultural Research, 20(7), 557–585.
- Wright, S. (1934). The method of path coefficients. The Annals of Mathematical Statistics, 5(3), 161–215. https://doi.org/10.1214/aoms/1177732676
- Dewey, D. R., & Lu, K. H. (1959). A correlation and path-coefficient analysis of components of crested wheatgrass seed production. Agronomy Journal, 51(9), 515–518. https://doi.org/10.2134/agronj1959.00021962005100090002x
- Li, C. C. (1956). The concept of path coefficient and its impact on population genetics. Biometrics, 12(2), 190–210. https://doi.org/10.2307/3001760
- Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
- Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879–891. https://doi.org/10.3758/BRM.40.3.879
- Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02