Calculate delta theta from a fitted coevfit object

Calculate \(\Delta\theta\) from a fitted coevfit object. \(\Delta\theta\) is defined as the difference in the equilibrium value for a "response" trait that results from a standardised increase in the value of another "predictor" trait. This value can be used to assess contingencies and directionality between variables in the coevolutionary process.

coev_calculate_delta_theta(object, response, predictor)

Arguments

object

An object of class coevfit

response

A character string equal to one of the coevolving variables in the model

predictor

A character string equal to one of the coevolving variables in the model

Value

Posterior samples in the draws_array format

Details

This function calculates \(\Delta\theta\), which is defined as the difference in the equilibrium value for a "response" trait that results from a standardised increase in the value of another "predictor" trait. The function first calculates the equilibrium trait value for the response trait when the predictor trait is held at its empirical median value (the coev_calculate_theta function is used for this purpose, see help(coev_calculate_theta) for further details). The function then calculates the equilibrium trait value for the response variable after increasing the predictor trait from its median by one median absolute deviation. The function then returns the posterior difference between these values. The resulting \(\Delta\theta\) samples can be used to infer whether increases in one trait have a positive or negative selective effect on another trait in the model.

References

Ringen, E., Martin, J. S., & Jaeggi, A. (2021). Novel phylogenetic methods reveal that resource-use intensification drives the evolution of "complex" societies. EcoEvoRXiv. doi:10.32942/osf.io/wfp95

Sheehan, O., Watts, J., Gray, R. D., Bulbulia, J., Claessens, S., Ringen, E. J., & Atkinson, Q. D. (2023). Coevolution of religious and political authority in Austronesian societies. Nature Human Behaviour, 7(1), 38-45. 10.1038/s41562-022-01471-y

See also

coev_calculate_delta_theta, coev_plot_delta_theta

Author

Scott Claessens scott.claessens@gmail.com, Erik Ringen erikjacob.ringen@uzh.ch

Examples

if (FALSE) { # \dontrun{
# fit dynamic coevolutionary model
fit <- coev_fit(
  data = authority$data,
  variables = list(
    political_authority = "ordered_logistic",
    religious_authority = "ordered_logistic"
  ),
  id = "language",
  tree = authority$phylogeny,
  # additional arguments for cmdstanr::sample()
  chains = 4,
  parallel_chains = 4,
  seed = 1
  )

# calculate delta theta
coev_calculate_delta_theta(
  object = fit,
  response = "political_authority",
  predictor = "religious_authority"
  )
} # }