Missingness mechanisms for multiple imputation

Specifications passed to the mechanism argument of gmm_impute(). They describe how an entry came to be missing, which sets the conditional the missing value is drawn from.

Usage

mar()

mnar(coord, beta, link = c("logit", "probit"))

censored(coord, lower = -Inf, upper = Inf)

Arguments

coord: Name or index of the single coordinate the mechanism acts on.
beta: Sensitivity slope of the log-odds (or probit score) of being missing in the missing value itself. Positive beta makes larger values more likely to be missing.
link: Selection link, "logit" (the default) or "probit".
lower, upper: Bounds of the interval a censored missing entry is known to lie in. At least one must be finite.

Value

A proxymix_gate object for gmm_impute().

Details

mar() is missing at random: the probability that an entry is missing may depend on the observed entries but not on the missing value, so the imputation conditional is the plain mixture conditional. This is the default.

censored() is a known interval. A missing entry of coord is known only to lie in [lower, upper] – a detection limit (upper = LOD), a ceiling (lower = cap), or interval censoring. The imputation conditional is the mixture conditional truncated to that interval, which proxymix evaluates in closed form, so the imputations respect the bound instead of substituting a constant such as half the detection limit.

mnar() is missing not at random through a selection model: an entry of coord is missing with probability \(g(\alpha + \beta\, y)\) in its own unobserved value \(y\), where \(g\) is the logistic or normal link. The slope beta is the sensitivity parameter and is supplied, not estimated – missing-not-at-random departures are not identified from the observed data, so the appropriate use is to posit beta, propagate it, and report how conclusions move with it (see proxy_mnar_sensitivity()). The intercept is calibrated to the observed missingness rate. beta = 0 is missing at random.

Examples

mar()
#> $type
#> [1] "mar"
#> 
#> attr(,"class")
#> [1] "proxymix_mar"  "proxymix_gate"
censored("y", upper = 0.5)             # a lower detection limit at 0.5
#> $type
#> [1] "censored"
#> 
#> $coord
#> [1] "y"
#> 
#> $lower
#> [1] -Inf
#> 
#> $upper
#> [1] 0.5
#> 
#> attr(,"class")
#> [1] "proxymix_censored" "proxymix_gate"    
mnar("y", beta = 0.8)                  # larger y more likely missing
#> $type
#> [1] "mnar"
#> 
#> $coord
#> [1] "y"
#> 
#> $beta
#> [1] 0.8
#> 
#> $link
#> [1] "logit"
#> 
#> attr(,"class")
#> [1] "proxymix_mnar" "proxymix_gate"