insight (version 1.0.0)

get_predicted_ci: Confidence intervals around predicted values

Description

Confidence intervals around predicted values

Usage

get_predicted_ci(x, ...)
# S3 method for default
get_predicted_ci(
  x,
  predictions = NULL,
  data = NULL,
  se = NULL,
  ci = 0.95,
  ci_type = "confidence",
  ci_method = NULL,
  dispersion_method = "sd",
  vcov = NULL,
  vcov_args = NULL,
  verbose = TRUE,
  ...
)

Arguments

x

A statistical model (can also be a data.frame, in which case the second argument has to be a model).

...

Other argument to be passed, for instance to get_predicted_ci().

predictions

A vector of predicted values (as obtained by stats::fitted(), stats::predict() or get_predicted()).

data

An optional data frame in which to look for variables with which to predict. If omitted, the data used to fit the model is used. Visualization matrices can be generated using get_datagrid().

se

Numeric vector of standard error of predicted values. If NULL, standard errors are calculated based on the variance-covariance matrix.

ci

The interval level. Default is NULL, to be fast even for larger models. Set the interval level to an explicit value, e.g. 0.95, for 95% CI).

ci_type

Can be "prediction" or "confidence". Prediction intervals show the range that likely contains the value of a new observation (in what range it would fall), whereas confidence intervals reflect the uncertainty around the estimated parameters (and gives the range of the link; for instance of the regression line in a linear regressions). Prediction intervals account for both the uncertainty in the model's parameters, plus the random variation of the individual values. Thus, prediction intervals are always wider than confidence intervals. Moreover, prediction intervals will not necessarily become narrower as the sample size increases (as they do not reflect only the quality of the fit). This applies mostly for "simple" linear models (like lm), as for other models (e.g., glm), prediction intervals are somewhat useless (for instance, for a binomial model for which the dependent variable is a vector of 1s and 0s, the prediction interval is... [0, 1]).

ci_method

The method for computing p values and confidence intervals. Possible values depend on model type.

• NULL uses the default method, which varies based on the model type.

• Most frequentist models: "wald" (default), "residual" or "normal".

• Bayesian models: "quantile" (default), "hdi", "eti", and "spi".

• Mixed effects lme4 models: "wald" (default), "residual", "normal", "satterthwaite", and "kenward-roger".

See get_df() for details.

dispersion_method

Bootstrap dispersion and Bayesian posterior summary: "sd" or "mad".

vcov

Variance-covariance matrix used to compute uncertainty estimates (e.g., for robust standard errors). This argument accepts a covariance matrix, a function which returns a covariance matrix, or a string which identifies the function to be used to compute the covariance matrix.

• A covariance matrix

• A function which returns a covariance matrix (e.g., stats::vcov())

• A string which indicates the kind of uncertainty estimates to return.

  • Heteroskedasticity-consistent: "HC", "HC0", "HC1", "HC2", "HC3", "HC4", "HC4m", "HC5". See ?sandwich::vcovHC

  • Cluster-robust: "CR", "CR0", "CR1", "CR1p", "CR1S", "CR2", "CR3". See ?clubSandwich::vcovCR

  • Bootstrap: "BS", "xy", "residual", "wild", "mammen", "fractional", "jackknife", "norm", "webb". See ?sandwich::vcovBS

  • Other sandwich package functions: "HAC", "PC", "CL", "OPG", "PL".

  • Kenward-Roger approximation: kenward-roger. See ?pbkrtest::vcovAdj.

vcov_args

List of arguments to be passed to the function identified by the vcov argument. This function is typically supplied by the sandwich or clubSandwich packages. Please refer to their documentation (e.g., ?sandwich::vcovHAC) to see the list of available arguments. If no estimation type (argument type) is given, the default type for "HC" equals the default from the sandwich package; for type "CR", the default is set to "CR3".

verbose

Toggle warnings.

Details

Typically, get_predicted() returns confidence intervals based on the standard errors as returned by the predict()-function, assuming normal distribution (+/- 1.96 * SE) resp. a Student's t-distribution (if degrees of freedom are available). If predict() for a certain class does not return standard errors (for example, merMod-objects), these are calculated manually, based on following steps: matrix-multiply X by the parameter vector B to get the predictions, then extract the variance-covariance matrix V of the parameters and compute XVX' to get the variance-covariance matrix of the predictions. The square-root of the diagonal of this matrix represent the standard errors of the predictions, which are then multiplied by the critical test-statistic value (e.g., ~1.96 for normal distribution) for the confidence intervals.

If ci_type = "prediction", prediction intervals are calculated. These are wider than confidence intervals, because they also take into account the uncertainty of the model itself. Before taking the square-root of the diagonal of the variance-covariance matrix, get_predicted_ci() adds the residual variance to these values. For mixed models, get_variance_residual() is used, while get_sigma()^2 is used for non-mixed models.

It is preferred to rely on standard errors returned by get_predicted() (i.e. returned by the predict()-function), because these are more accurate than manually calculated standard errors. Use get_predicted_ci() only if standard errors are not available otherwise. An exception are Bayesian models or bootstrapped predictions, where get_predicted_ci() returns quantiles of the posterior distribution or bootstrapped samples of the predictions. These are actually accurate standard errors resp. confidence (or uncertainty) intervals.

Examples

if (FALSE) { # require("boot") && require("datawizard") && require("bayestestR")
# Confidence Intervals for Model Predictions
# ------------------------------------------

data(mtcars)

# Linear model
# ------------
x <- lm(mpg ~ cyl + hp, data = mtcars)
predictions <- predict(x)
ci_vals <- get_predicted_ci(x, predictions, ci_type = "prediction")
head(ci_vals)
ci_vals <- get_predicted_ci(x, predictions, ci_type = "confidence")
head(ci_vals)
ci_vals <- get_predicted_ci(x, predictions, ci = c(0.8, 0.9, 0.95))
head(ci_vals)

# Bootstrapped
# ------------
predictions <- get_predicted(x, iterations = 500)
get_predicted_ci(x, predictions)

ci_vals <- get_predicted_ci(x, predictions, ci = c(0.80, 0.95))
head(ci_vals)
datawizard::reshape_ci(ci_vals)

ci_vals <- get_predicted_ci(x,
  predictions,
  dispersion_method = "MAD",
  ci_method = "HDI"
)
head(ci_vals)


# Logistic model
# --------------
x <- glm(vs ~ wt, data = mtcars, family = "binomial")
predictions <- predict(x, type = "link")
ci_vals <- get_predicted_ci(x, predictions, ci_type = "prediction")
head(ci_vals)
ci_vals <- get_predicted_ci(x, predictions, ci_type = "confidence")
head(ci_vals)
}