set_restrictions: Restrict a model

Description

Restrict a model's parameter space. This reduces the number of nodal types and in consequence the number of unit causal types.

Usage

set_restrictions(
  model,
  statement = NULL,
  join_by = "|",
  labels = NULL,
  keep = FALSE
)

Arguments

model

A causal_model. A model object generated by make_model.

statement

A quoted expressions defining the restriction. If values for some parents are not specified, statements should be surrounded by parentheses, for instance (Y[A = 1] > Y[A=0]) will be interpreted for all combinations of other parents of Y set at possible levels they might take.

join_by

A string. The logical operator joining expanded types when statement contains wildcard (.). Can take values '&' (logical AND) or '|' (logical OR). When restriction contains wildcard (.) and join_by is not specified, it defaults to '|', otherwise it defaults to NULL. Note that join_by joins within statements, not across statements.

labels

A list of character vectors specifying nodal types to be kept or removed from the model. Use get_nodal_types to see syntax. Note that labels gets overwritten by statement if statement is not NULL.

keep

Logical. If `FALSE`, removes and if `TRUE` keeps only causal types specified by statement or labels.

Value

An object of class model. The causal types and nodal types in the model are reduced according to the stated restriction.

Details

Restrictions are made to nodal types, not to unit causal types. Thus for instance in a model X -> M -> Y, one cannot apply a simple restriction so that Y is nondecreasing in X, however one can restrict so that M is nondecreasing in X and Y nondecreasing in M. To have a restriction that Y be nondecreasing in X would otherwise require restrictions on causal types, not nodal types, which implies a form of undeclared confounding (i.e. that in cases in which M is decreasing in X, Y is decreasing in M).

Since restrictions are to nodal types, all parents of a node are implicitly fixed. Thus for model make_model(`X -> Y <- W`) the request set_restrictions(`(Y[X=1] == 0)`) is interpreted as set_restrictions(`(Y[X=1, W=0] == 0 | Y[X=1, W=1] == 0)`).

Statements with implicitly controlled nodes should be surrounded by parentheses, as in these examples.

Note that prior probabilities are redistributed over remaining types.

Examples

Run this code

# NOT RUN {
# 1. Restrict parameter space using statements
model <- make_model('X->Y') %>%
  set_restrictions(statement = c('X[] == 0'))

model <- make_model('X->Y') %>%
  set_restrictions(non_increasing('X', 'Y'))

model <- make_model('X -> Y <- W') %>%
  set_restrictions(c(decreasing('X', 'Y'), substitutes('X', 'W', 'Y')))

model$parameters_df

model <- make_model('X-> Y <- W') %>%
  set_restrictions(statement = decreasing('X', 'Y'))
model$parameters_df

model <- make_model('X->Y') %>%
  set_restrictions(decreasing('X', 'Y'))
model$parameters_df

model <- make_model('X->Y') %>%
  set_restrictions(c(increasing('X', 'Y'), decreasing('X', 'Y')))
model$parameters_df
# }
# NOT RUN {
# Restrict to define a model with monotonicity
model <- make_model('X->Y') %>%
set_restrictions(statement = c('Y[X=1] < Y[X=0]'))
get_parameter_matrix(model)

# Restrict to a single type in endogenous node
model <- make_model('X->Y') %>%
set_restrictions(statement =  '(Y[X = 1] == 1)', join_by = '&', keep = TRUE)
get_parameter_matrix(model)

#  Use of | and &
# Keep node if *for some value of B* Y[A = 1] == 1
model <- make_model('A->Y<-B') %>%
set_restrictions(statement =  '(Y[A = 1] == 1)', join_by = '|', keep = TRUE)
dim(get_parameter_matrix(model))


# Keep node if *for all values of B* Y[A = 1] == 1
model <- make_model('A->Y<-B') %>%
set_restrictions(statement =  '(Y[A = 1] == 1)', join_by = '&', keep = TRUE)
dim(get_parameter_matrix(model))

# Restrict multiple nodes
model <- make_model('X->Y<-M; X -> M' ) %>%
set_restrictions(statement =  c('(Y[X = 1] == 1)', '(M[X = 1] == 1)'), join_by = '&', keep = TRUE)
get_parameter_matrix(model)

# Restrictions on levels for endogenous nodes aren't allowed
model <- make_model('X->Y') %>%
set_restrictions(statement =  '(Y == 1)')


# 2. Restrict parameter space Using labels:
model <- make_model('X->Y') %>%
set_restrictions(labels = list(X = '0', Y = '00'))

# Restrictions can be  with wildcards
model <- make_model('X->Y') %>%
set_restrictions(labels = list(Y = '?0'))
get_parameter_matrix(model)

# Running example: there are only four causal types
model <- make_model('S -> C -> Y <- R <- X; X -> C -> R') %>%
set_restrictions(labels = list(C = '1000', R = '0001', Y = '0001'), keep = TRUE)
get_parameter_matrix(model)
# }