sjstats (version 0.17.6)

se: Standard Error for variables or coefficients

Description

Compute standard error for a variable, for all variables of a data frame, for joint random and fixed effects coefficients of (non-/linear) mixed models, the adjusted standard errors for generalized linear (mixed) models, or for intraclass correlation coefficients (ICC).

Usage

se(x, ...)

Arguments

x

(Numeric) vector, a data frame, an lm, glm, merMod (lme4), or stanreg model object, an ICC object (as obtained by the icc-function), a table or xtabs object, or a list with estimate and p-value. For the latter case, the list must contain elements named estimate and p.value (see 'Examples' and 'Details').

...

Currently not used.

Value

The standard error of x.

Details

Standard error for variables

For variables and data frames, the standard error is the square root of the variance divided by the number of observations (length of vector).

Standard error for mixed models

For linear mixed models, and generalized linear mixed models, this function computes the standard errors for joint (sums of) random and fixed effects coefficients (unlike se.coef, which returns the standard error for fixed and random effects separately). Hence, se() returns the appropriate standard errors for coef.merMod.

Standard error for generalized linear models

For generalized linear models, approximated standard errors, using the delta method for transformed regression parameters are returned (Oehlert 1992).

Standard error for proportions and mean value

To compute the standard error for relative frequencies (i.e. proportions, or mean value if x has only two categories), this vector must be supplied as table, e.g. se(table(iris$Species)). se() than computes the relative frequencies (proportions) for each value and the related standard error for each value. This might be useful to add standard errors or confidence intervals to descriptive statistics. If standard errors for weighted variables are required, use xtabs(), e.g. se(xtabs(weights ~ variable)).

Standard error for regression coefficient and p-value

se() also returns the standard error of an estimate (regression coefficient) and p-value, assuming a normal distribution to compute the z-score from the p-value (formula in short: b / qnorm(p / 2)). See 'Examples'.

References

Oehlert GW. 1992. A note on the delta method. American Statistician 46(1).

Gelman A 2017. How to interpret confidence intervals? http://andrewgelman.com/2017/03/04/interpret-confidence-intervals/

Examples

# NOT RUN {
library(lme4)
library(sjmisc)

# compute standard error for vector
se(rnorm(n = 100, mean = 3))

# compute standard error for each variable in a data frame
data(efc)
se(efc[, 1:3])

# compute standard error for merMod-coefficients
library(lme4)
fit <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
se(fit)

# compute odds-ratio adjusted standard errors, based on delta method
# with first-order Taylor approximation.
data(efc)
efc$services <- sjmisc::dicho(efc$tot_sc_e, dich.by = 0)
fit <- glm(
  services ~ neg_c_7 + c161sex + e42dep,
  data = efc,
  family = binomial(link = "logit")
)
se(fit)

# compute odds-ratio adjusted standard errors for generalized
# linear mixed model, also based on delta method

# create binary response
sleepstudy$Reaction.dicho <- dicho(sleepstudy$Reaction, dich.by = "median")
fit <- glmer(
  Reaction.dicho ~ Days + (Days | Subject),
  data = sleepstudy,
  family = binomial("logit")
)
se(fit)

# compute standard error for proportions
efc$e42dep <- to_label(efc$e42dep)
se(table(efc$e42dep))

# including weights
efc$weights <- rnorm(nrow(efc), 1, .25)
se(xtabs(efc$weights ~ efc$e42dep))

# compute standard error from regression coefficient and p-value
se(list(estimate = .3, p.value = .002))

# }
# NOT RUN {
# compute standard error of ICC for the linear mixed model
icc(fit)
se(icc(fit))

# the standard error for the ICC can be computed manually in this way,
# taking the fitted model example from above
library(dplyr)
library(purrr)
dummy <- sleepstudy %>%
  # generate 100 bootstrap replicates of dataset
  bootstrap(100) %>%
  # run mixed effects regression on each bootstrap replicate
  # and compute ICC for each "bootstrapped" regression
  mutate(
    models = map(strap, ~lmer(Reaction ~ Days + (Days | Subject), data = .x)),
    icc = map_dbl(models, ~icc(.x))
  )

# now compute SE and p-values for the bootstrapped ICC, values
# may differ from above example due to random seed
boot_se(dummy, icc)
boot_p(dummy, icc)
# }
# NOT RUN {

# }