summary.tinyVAST function

summarize tinyVAST

summarize parameters from a fitted tinyVAST

## S3 method for class 'tinyVAST'
summary(
  object,
  what = c("space_term", "time_term", "spacetime_term", "fixed"),
  predictor = c("one", "two"),
  ...
)

Arguments

• object: Output from tinyVAST()
• what: What component to summarize, whether space_term, spacetime_term, or fixed for the fixed effects included in the GAM formula
• predictor: whether to get the 1st or 2nd linear predictor (the latter is only applicable in delta models)
• ...: Not used

Returns

A data-frame containing the estimate (and standard errors, two-sided Wald-test z-value, and associated p-value if the standard errors are available) for model parameters, including the fixed-effects specified via formula, or the path coefficients for the spatial SEM specified via space_term, the dynamic SEM specified via time_term, or the spatial dynamic SEM specified via spacetime_term

Details

tinyVAST includes three components:

• Space-variable interaction: a separable Gaussian Markov random field (GMRF) constructed from a structural equation model (SEM) and a spatial variable
• Space-variable-time interaction: a separable GMRF constructed from a a dynamic SEM (a nonseparable time-variable interaction) and a spatial variable
• Additive variation: a generalized additive model (GAM), representing exogenous covariates

Each of these are summarized and interpreted differently, and summary.tinyVAST

facilitates this.

Regarding the DSEM componennt, tinyVAST includes an "arrow and lag" notation, which specifies the set of path coefficients and exogenous variance parameters to be estimated. Function tinyVAST

then estimates the maximum likelihood value for those coefficients and parameters by maximizing the log-marginal likelihood.

However, many users will want to associate individual parameters and standard errors with the path coefficients that were specified using the "arrow and lag" notation. This task is complicated in models where some path coefficients or variance parameters are specified to share a single value a priori, or were assigned a name of NA and hence assumed to have a fixed value a priori (such that these coefficients or parameters have an assigned value but no standard error). The summary function therefore compiles the MLE for coefficients (including duplicating values for any path coefficients that assigned the same value) and standard error estimates, and outputs those in a table that associates them with the user-supplied path and parameter names. It also outputs the z-score and a p-value arising from a two-sided Wald test (i.e. comparing the estimate divided by standard error against a standard normal distribution).