Path analysis and D-square analysis are statistical methods used to evaluate the relationships between variables in a model. Both methods are typically used with replicated data, where multiple observations are taken for each variable. However, it is possible to perform path analysis and D-square analysis with unreplicated data, but it will require making certain assumptions about the data and the model.

One way to perform path analysis with unreplicated data is by using simulation methods. This approach involves generating simulated data that is consistent with the assumptions of the model and then estimating the parameters of the model using the simulated data.

Another way to perform path analysis with unreplicated data is by using bootstrapping. Bootstrapping involves resampling the data with replacement to create multiple sets of pseudo-replicated data, then analyzing each set of data separately and combining the results.

D-square analysis is a technique that is used to evaluate the proportion of variance in a dependent variable that is explained by a set of independent variables. When applied to unreplicated data, D-square analysis requires assumptions about the population and the sampling process, for example assuming the sample is a random sample from the population, and using that to estimate the population parameters.

It is important to note that, in both cases, the results from the analysis are based on assumptions and may not accurately reflect the true relationships in the population. It is always recommended to use replicated data if possible for more robust results.

Path analysis and D-square analysis can be performed on unreplicated data using simulation methods, traditional methods, or by estimating path coefficients for simple models given correlation and/or regression coefficients. The path-coefficient analysis measures the direct effect of one variable on another, allowing the separation of direct and indirect effects. Variance covariance analysis is an extension of the regression model used to test the fit of a correlation matrix against two or more causal models.