bdsm (version 0.1.1)

SEM_likelihood: Likelihood for the SEM model

Description

Likelihood for the SEM model

Usage

SEM_likelihood(
  params,
  data,
  timestamp_col,
  entity_col,
  dep_var_col,
  lin_related_regressors = NULL,
  per_entity = FALSE,
  exact_value = TRUE
)

Value

The value of the likelihood for SEM model (or a part of interest of the likelihood)

Arguments

params

Parameters describing the model. Can be either a vector or a list with named parameters. See 'Details'

data

Data for the likelihood computations. Can be either a list of matrices or a dataframe. If the dataframe, additional parameters are required to build the matrices within the function.

timestamp_col

Column which determines time stamps. For now only natural numbers can be used.

entity_col

Column which determines entities (e.g. countries, people)

dep_var_col

Column with dependent variable

lin_related_regressors

Which subset of columns should be used as regressors for the current model. In other words regressors are the total set of regressors and lin_related_regressors are the ones for which linear relation is not set to zero for a given model.

per_entity

Whether to compute overall likelihood or a vector of likelihoods with per entity value

exact_value

Whether the exact value of the likelihood should be computed (TRUE) or just the proportional part (FALSE). Currently TRUE adds: 1. a normalization constant coming from Gaussian distribution, 2. a term disappearing during likelihood simplification in Likelihood-based Estimation of Dynamic Panels with Predetermined Regressors by Moral-Benito (see Appendix A.1). The latter happens when transitioning from equation (47) to equation (48), in step 2: the term trace(HG_22) is dropped, because it can be assumed to be constant from Moral-Benito perspective. To get the exact value of the likelihood we have to take this term into account.

Details

The params argument is a list that should contain the following components:

alpha scalar value which determines linear dependence on lagged dependent variable

phi_0 scalar value which determines linear dependence on the value of dependent variable at the lowest time stamp

err_var scalar value which determines classical error component (Sigma11 matrix, sigma_epsilon^2)

dep_vars double vector of length equal to the number of time stamps (i.e. time stamps greater than or equal to the second lowest time stamp)

beta double vector which determines the linear dependence on regressors different than the lagged dependent variable; The vector should have length equal to the number of regressors.

phi_1 double vector which determines the linear dependence on initial values of regressors different than the lagged dependent variable; The vector should have length equal to the number of regressors.

phis double vector which together with psis determines upper right and bottom left part of the covariance matrix; The vector should have length equal to the number of regressors times number of time stamps minus 1, i.e. regressors_n * (periods_n - 1)

psis double vector which together with psis determines upper right and bottom left part of the covariance matrix; The vector should have length equal to the number of regressors times number of time stamps minus 1 times number of time stamps divided by 2, i.e. regressors_n * (periods_n - 1) * periods_n / 2

Examples

set.seed(1)
df <- data.frame(
  entities = rep(1:4, 5),
  times = rep(seq(1960, 2000, 10), each = 4),
  dep_var = stats::rnorm(20), a = stats::rnorm(20), b = stats::rnorm(20)
)
df <-
  feature_standardization(df, timestamp_col = times, entity_col = entities)
SEM_likelihood(0.5, df, times, entities, dep_var)