Calculate pseudo-residuals for discrete-valued observations
pseudo_res_discrete.Rd
For HMMs, pseudo-residuals are used to assess the goodness-of-fit of the model. These are based on the cumulative distribution function (CDF) $$F_{X_t}(x_t) = F(x_t \mid x_1, \dots, x_{t-1}, x_{t+1}, \dots, x_T)$$ and can be used to quantify whether an observation is extreme relative to its model-implied distribution.
This function calculates such residuals for discrete-valued observations, based on the local state probabilities obtained by stateprobs
or stateprobs_g
and the respective parametric family.
Usage
pseudo_res_discrete(
obs,
stateprobs,
dist,
par,
normal = TRUE,
randomise = TRUE,
seed = NULL
)
Arguments
- obs
vector of discrete-valued observations (of length n)
- stateprobs
matrix of local state probabilities for each observation (of dimension c(n,N), where N is the number of states)
- dist
character string specifying which parametric CDF to use (e.g.,
"norm"
for normal or"pois"
for Poisson)- par
named parameter list for the parametric CDF
Names need to correspond to the parameter names in the specified distribution (e.g.
list(mean = c(1,2), sd = c(1,1))
for a normal distribution and 2 states). This argument is as flexible as the parametric distribution allows. For example you can have a matrix of parameters with one row for each observation and one column for each state.- normal
logical, if
TRUE
, returns Gaussian pseudo residualsThese will be approximately standard normally distributed if the model is correct.
- randomise
logical, if
TRUE
, return randomised pseudo residuals. Recommended for discrete observations.- seed
integer, seed for random number generation
Details
For discrete observations, calculating pseudo residuals is slightly more involved, as the CDF is a step function.
Therefore, one can calculate the lower and upper CDF values for each observation.
By default, this function does exactly that and then randomly samples the interval in between to give approximately Gaussian psuedo-residuals.
If randomise
is set to FALSE
, the lower, upper and mean pseudo-residuasl are returned.