hplm: Hierarchical piecewise linear model / piecewise regression...

In scan: Single-Case Data Analyses for Single and Multiple Baseline Designs

Hierarchical piecewise linear model / piecewise regression for multiple cases

Description

The hplm() function computes a hierarchical piecewise regression model. It extends the standard piecewise regression model to multiple cases by estimating fixed and random effects. The function uses the lme function of the nlme package to fit linear mixed-effects models. The model can include random intercepts and random slopes for level, trend, and treatment effects. Additionally, it allows for the inclusion of autoregressive structures and unequal variances across phases. The function also provides options for likelihood ratio tests to compare models with and without random slope effects, as well as the calculation of intraclass correlations (ICC) to assess the proportion of variance attributable to between-case differences. This function is particularly useful for analyzing data from multiple single-case experimental designs (SCEDs) where observations are nested within cases.

Usage

hplm(
  data,
  dvar,
  pvar,
  mvar,
  model = c("W", "H-M", "B&L-B", "JW"),
  contrast = c("first", "preceding"),
  contrast_level = NA,
  contrast_slope = NA,
  method = c("ML", "REML"),
  control = list(opt = "optim"),
  random.slopes = FALSE,
  lr.test = FALSE,
  ICC = TRUE,
  trend = TRUE,
  level = TRUE,
  slope = TRUE,
  random_trend = FALSE,
  random_level = FALSE,
  random_slope = FALSE,
  fixed = NULL,
  random = NULL,
  ar = 0,
  unequal_variances = FALSE,
  update.fixed = NULL,
  data.l2 = NULL,
  ...
)

## S3 method for class 'sc_hplm'
print(x, digits = 3, bcsmd = FALSE, casewise = FALSE, ...)

## S3 method for class 'sc_hplm'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  round = 2,
  nice = TRUE,
  casewise = FALSE,
  ...
)

## S3 method for class 'sc_hplm'
coef(object, casewise = FALSE, ...)

Arguments

data	A single-case data frame. See scdf() to learn about this format.
dvar	Character string with the name of the dependent variable. Defaults to the attributes in the scdf file.
pvar	Character string with the name of the phase variable. Defaults to the attributes in the scdf file.
mvar	Character string with the name of the measurement time variable. Defaults to the attributes in the scdf file.
model	Model used for calculating the dummy parameters (see Huitema & McKean, 2000). Default is model = "W". Possible values are: "B&L-B", "H-M", "W", and deprecated "JW".
contrast	Sets contrast_level and contrast_slope. Either "first", "preceding" or a contrast matrix. If NA contrast is ignored.
contrast_level	Either "first", "preceding" or a contrast matrix. If NA contrast_level is a copy of contrast.
contrast_slope	Either "first", "preceding" or a contrast matrix. If NA contrast_level is a copy of contrast.
method	Method used to fit your model. Pass "REML" to maximize the restricted log-likelihood or "ML" for maximized log-likelihood. Default is "ML".
control	A list of settings for the estimation algorithm, replacing the default values passed to the function lmeControl of the nlme package.
random.slopes	If random.slopes = TRUE random slope effects of the level, trend, and treatment parameter are estimated.
lr.test	If set TRUE likelihood ratio tests are calculated comparing model with vs. without random slope parameters.
ICC	If ICC = TRUE an intraclass-correlation is estimated.
trend	A logical indicating if a trend parameters is included in the model.
level	A logical indicating if a level parameters is included in the model.
slope	A logical indicating if a slope parameters is included in the model.
random_trend	If TRUE, includes a random trend trend effect.
random_level	If TRUE, includes a random level trend effect.
random_slope	If TRUE, includes a random slope trend effect.
fixed	Defaults to the fixed part of the standard piecewise regression model. The parameter phase followed by the phase name (e.g., phaseB) indicates the level effect of the corresponding phase. The parameter 'inter' followed by the phase name (e.g., interB) adresses the slope effect based on the method provide in the model argument (e.g., "B&L-B"). The formula can be changed for example to include further L1 or L2 variables into the regression model.
random	The random part of the model. Defaults to a random intercept model. The formula can be changed to include random slope effects for level, trend, and treatment effects.
ar	Maximal lag of autoregression. Modelled based on the Autoregressive-Moving Average (ARMA) function.
unequal_variances	Logical. If set TRUE, estimations are weighted by phase variances.
update.fixed	An easier way to change the fixed model part (e.g., . ~ . + newvariable).
data.l2	A data frame providing additional variables at Level 2. The scdf File has to have names for all cases and the Level 2 data frame has to have a column named 'cases' with the names of the cases the Level 2 variables belong to.
...	Further arguments passed to the lme function.
x	An object returned by hplm()
digits	The minimum number of significant digits to be use. If set to "auto" (default), values are predefined.
bcsmd	If TRUE, reports between-case standardized mean differences.
casewise	Returns the estimations for each case separately
object	An scdf or an object exported from a scan function.
caption	Character string with table caption. If left NA (default) a caption will be created based on the exported object.
footnote	Character string with table footnote. If left NA (default) a footnote will be created based on the exported object.
filename	String containing the file name. If a filename is given the output will be written to that file.
round	Integer passed to the digits argument used to round values.
nice	If set TRUE (default) output values are rounded and optimized for publication tables.

Value

An object of class sc_hplm.

• model | List containing infromation about

• N | Number of single-cases.

• formula | A list containing the fixed and the random formulas of the hplm model.

• hplm | Object of class lme contaning the multilevel model.

• model.0 | Object of class lme containing the zero model.

• ICC | List containing intraclass correlation and test parameters.

• model.without | Object of class gls containing the fixed effect model.

• contrast | List with contrast definitions.

Functions

• print(sc_hplm): Print results

• export(sc_hplm): Export results as html table (see export())

• coef(sc_hplm): Extract model coefficients

Model specification

The fixed effects part of the model can be specified using the fixed argument, while the random effects part can be specified using the random argument. If not provided, default formulas based on the specified model type (e.g., "B&L-B") are created. The function also allows for the inclusion of autoregressive structures through the ar argument and unequal variances across phases through the unequal_variances argument.

Random slopes

By setting the random.slopes argument to TRUE, the model will include random slope effects for level, trend, and treatment effects. This allows for individual differences in how cases respond to these effects.

Likelihood ratio tests

If the lr.test argument is set to TRUE, the function will perform likelihood ratio tests to compare models with and without random slope effects. This helps to determine whether including random slopes significantly improves model fit.

Intraclass correlation

If the ICC argument is set to TRUE, the function will calculate the intraclass correlation coefficient (ICC) to assess the proportion of variance attributable to between-case differences. This provides insight into the degree of similarity among observations within the same case.

Author(s)

Juergen Wilbert

See Also

Other regression functions: bplm(), fetch(), mplm(), plm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

## Compute hplm model on a MBD over fifty cases (restricted log-likelihood)
hplm(exampleAB_50, method = "REML", random.slopes = FALSE)

## Analyzing with additional L2 variables
Leidig2018 |>
  add_l2(Leidig2018_l2) |>
  hplm(update.fixed = .~. + gender + migration + ITRF_TOTAL*phaseB,
       slope = FALSE, random.slopes = FALSE, lr.test = FALSE
  )

scan documentation built on April 1, 2026, 9:06 a.m.