Influence measures by case deletion

Refits the model with one group (or observation) left out at a time, warm-started at the full-data estimates, and collects the fixed-effect and covariance-parameter changes. cooks.distance() on the result gives the scaled fixed-effect displacement (calling it on the fit itself runs influence() first); dfbeta() and dfbetas() give the per-unit coefficient changes, raw and scaled by the coefficient standard errors (the lme4 influence surface). plot.frmtmb_influence() draws all three.

Usage

# S3 method for class 'frmtmb_fit'
influence(model, groups = NULL, data = NULL, force = FALSE, ...)

# S3 method for class 'frmtmb_fit'
cooks.distance(model, ...)

# S3 method for class 'frmtmb_influence'
dfbeta(model, ...)

# S3 method for class 'frmtmb_influence'
dfbetas(model, ...)

Arguments

model

A frmtmb_fit.

groups

Name of a random-effect grouping factor (see ngrps()) to delete level-wise; NULL deletes single observations (refuses for large n unless force = TRUE).

data

The original model data. The default is the data the fit holds: the model frame and the variables the formula reads through a transform (x of poly(x, 2) or log(x)), on the rows the fit used. A data-dependent basis (poly(), splines::ns(), scale()) keeps the knots, coefficients or center of the fit in every deletion refit, as in lme4's influence.merMod(), so a coefficient change is not a change of basis.

force

Allow observation-wise deletion for n > 500.

...

Refused: an argument the method does not have is an error naming it, rather than silently changing nothing.

Value

A frmtmb_influence object: fixed and theta matrices (one row per deleted unit) plus the full-data reference.

Details

Each deletion refits the same model, so an ordinal response keeps the threshold count of the full-data fit, and the per-level counts of thres(gr = ), whether the response is coded as integers, as a character vector or as an ordered factor. Deleting the last observation in ANY category, bottom, interior or top, leaves that category's threshold in the model and unidentified, which shows as a large displacement in its column, never as a shorter row or a coefficient under the next column's name.

Two deletions cannot refit the fitted model at all and are refused by name. A groups = deletion that removes a whole level of thres(gr = ) takes away every observation behind that level's thresholds, so they could only be invented. data = holding a response category outside the fitted model's threshold layout, or a thres(gr = ) level the fit never saw, describes a different model. A category the fit never OBSERVED is not outside that layout when thres(K) declared it, so data = may reach one of those.

A refit that fails for any reason, these two included, leaves its row NA, and the failures are counted. When some units failed the table comes back with a warning carrying the count and the first reason; when every unit failed there is no table to hand back, so that first reason is raised as an error instead of a silent matrix of NA.

Examples

# \donttest{
set.seed(7)
dd <- data.frame(x = rnorm(60), g = factor(rep(1:6, 10)))
dd$y <- rnorm(60, 1 + 0.5 * dd$x + rnorm(6, 0, 0.5)[dd$g], 1)
fit <- frm(bf(y ~ x + (1 | g)) + gaussian(), data = dd)
#> Boundary (singular) fit: sd_g__Intercept is at zero. The likelihood does not change as it moves further that way, so it has no standard error (NaN in summary(), vcov() and confint()); the other standard errors are kept. lme4 reports such a fit as singular; diagnose() lists the components at the boundary
infl <- influence(fit, groups = "g")
cooks.distance(infl)
#>          1          2          3          4          5          6 
#> 0.04211219 0.49008215 0.04168487 0.12687100 0.02619522 0.18339082 
# }