Applies the Delta method to calculate the standard errors of transformations of parameters.
apollo_deltaMethod(model, deltaMethod_settings)Invisibly returns a matrix containing the value, standard error and t-ratio resulting from the requested expression or operation. If printPVal is not FALSE, p-values are also included. If allPairs=TRUE, invisibly returns a list containing the requested expression/operation output, if any, as well as matrices of values, standard errors and t-ratios for all pairwise ratios and differences. Results are also printed to screen, and pairwise results are written to CSV files when allPairs=TRUE.
Model object. Estimated model object as returned by function apollo_estimate.
List. Contains settings for this function. User input is required for all settings except those with a default or marked as optional.
expression: Character vector. A character vector with a single or multiple arbitrary functions of the estimated parameters, as text.
For example: c(VTT="b1/b2*60"). Each expression can only contain model parameters (estimated or fixed),
numeric values, and operands. At least one of the parameters used needs to not have been fixed in estimation. Variables in the database
cannot be included. If the user does not provide a name for an expression, then the expression itself is used in the output. If this setting is provided, then operation,
parName1, parName2, multPar1 and multPar2 are
ignored.
allPairs: Logical. If set to TRUE, Delta method calculations are carried out for the ratio and difference for all pairs of parameters and returned as two separate matrices with values and t-ratios. FALSE by default.
varcov: Character. Type of variance-covariance matrix to use in calculations.
It can take values "classical", "robust" and
"bootstrap". Default is "robust".
printPVal: Logical or Scalar. TRUE or 1 for printing p-values for one-sided test, 2 for printing p-values for two-sided test, FALSE for not printing p-values. FALSE by default.
operation: Character. Function to calculate the delta method for. See details. Not used if expression is provided.
parName1: Character. Name of the first parameter if operation is used. See details. Not used if expression is provided.
parName2: Character. Name of the second parameter if operation is used. See details. Not used if expression is provided.. Optional depending on operation.
multPar1: Numeric scalar. An optional value to scale parName1. Not used if expression is provided. Default is 1.
multPar2: Numeric scalar. An optional value to scale parName2. Not used if expression is provided. Default is 1.
apollo_deltaMethod can be used in two ways. The first and recommended way is to provide an
element called expression inside its argument deltaMethod_settings. expression
should contain the expression or expressions for which the standard error is/are to be calculated, as text. For
example, to calculate the ratio between parameters b1 and b2, expression=c(vtt="b1/b2") should be used.
The second method is to provide the name of a specific operation inside deltaMethod_settings.
The following seven operations are supported.
diff: Calculates the s.e. of parName1 - parName2 and parName2 - parName1
exp: Calculates the s.e. of exp(parName1)
logistic: If only parName1 is provided, it calculates the s.e. of
exp(parName1)/(1+exp(parName1)) and 1/(1+exp(parName1)).
If parName1 and parName2 are provided, it calculates
exp(par_i)/(1+exp(parName1)+exp(parName2)) for i=1, 2, and 3 (par_3 = 1).
lognormal: Calculates the mean and s.d. of a lognormal distribution based on the mean
(parName1) and s.d. (parName2) of the underlying normal.
prod: Calculates the s.e. of parName1*parName2
ratio: Calculates the s.e. of parName1/parName2 and parName2/parName1
sum: Calculates the s.e. of parName1 + parName2
By default, apollo_deltaMethod uses the robust covariance matrix. However, the user can change this through the varcov setting.