Package 'lmeInfo'

Bryant et al. (2016)

Description

Data from a multi-level multiple baseline design conducted by Bryant et al. (2016). The study involved collecting repeated measures of math performance on twelve students nested in three schools. The variables are as follows:

• Study_ID Study identifier.

• school School identifier.

• case Student identifier.

• session Measurement occasion.

• treatment Indicator for treatment phase.

• outcome Texas Early Mathematics Inventory (TEMI-Aim Check) scores.

• trt_time Measurement occasion times treatment phase.

• session_c Measurement occasion centered at the follow-up time (Measurement occasion 9).

Format

A data frame with 299 rows and 8 variables

Source

Bryant, B. R., Bryant, D. P., Porterfield, J., Dennis, M. S., Falcomata, T., Valentine, C., Brewer, C., & Bell, K. (2016). The effects of a Tier 3 intervention on the mathematics performance of second grade students with severe mathematics difficulties. Journal of Learning Disabilities, 49(2), 176-188. doi:10.1177/0022219414538516

---

Calculates a confidence interval for a standardized mean difference effect size

Description

Calculates a confidence interval for a g_mlm object, using either a central t distribution (for a symmetric interval) or a non-central t distribution (for an asymmetric interval).

Usage

CI_g(g, cover = 0.95, bound = 35, symmetric = TRUE)

Arguments

g	an estimated effect size object of class g_mlm.
cover	confidence level.
bound	numerical tolerance for non-centrality parameter in qt.
symmetric	If TRUE (the default), use a symmetric confidence interval. If FALSE, use a non-central t approximation to obtain an asymmetric confidence interval.

Value

A vector of lower and upper confidence bounds.

Examples

library(nlme)
data(Bryant2016, package = "lmeInfo")
Bryant2016_RML1 <- lme(fixed = outcome ~ treatment,
                       random = ~ 1 | school/case,
                       correlation = corAR1(0, ~ session | school/case),
                       data = Bryant2016)
Bryant2016_g1 <- g_mlm(Bryant2016_RML1, p_const = c(0,1), r_const = c(1,1,0,1),
                       infotype = "expected")
CI_g(Bryant2016_g1, symmetric = TRUE)
CI_g(Bryant2016_g1, symmetric = FALSE)

---

Extract estimated variance components

Description

Extracts the estimated variance components from a fitted linear mixed effects model (lmeStruct object) or generalized least squares model (glsStruct object).

Usage

extract_varcomp(mod, separate_variances, vector)

Arguments

mod	Fitted model of class lmeStruct or glsStruct.
separate_variances	Logical indicating whether to return the separate level-1 variance components for each stratum if using varIdent function to allow for different variances per stratum. Default is FALSE.
vector	Logical indicating whether to return the variance components as a numeric vector. Default is FALSE.

Value

If vector = FALSE, an object of class varcomp consisting of a list of estimated variance components. Models that do not include correlation structure parameters or variance structure parameters will have empty lists for those components. If vector = TRUE, a numeric vector of estimated variance components.

If separate_variances = TRUE and if weights = varIdent(form = ~ 1 | Stratum) is specified in the model fitting, separate level-1 variance estimates will be returned for each stratum. If separate_variances = TRUE but if the weighting structure is not specified with varIdent, or if separate_variances = FALSE, then no separate level-1 variance estimates will be returned.

Examples

library(nlme)
data(Bryant2016)
Bryant2016_RML <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      weights = varIdent(form = ~ 1 | treatment),
                      data = Bryant2016)
extract_varcomp(Bryant2016_RML, separate_variances = FALSE)
extract_varcomp(Bryant2016_RML, separate_variances = TRUE)
extract_varcomp(Bryant2016_RML, vector = TRUE)

---

Calculate expected, observed, or average Fisher information matrix

Description

Calculates the expected, observed, or average Fisher information matrix from a fitted linear mixed effects model (lmeStruct object) or generalized least squares model (glsStruct object).

Usage

Fisher_info(mod, type = "expected", separate_variances = FALSE)

Arguments

mod	Fitted model of class lmeStruct or glsStruct.
type	Type of information matrix. One of "expected" (the default), "observed", or "average".
separate_variances	Logical indicating whether to return the Fisher information matrix for separate level-1 variance components if using varIdent function to allow for different variances per stratum. Default is FALSE.

Value

Information matrix corresponding to variance component parameters of mod.

If separate_variances = TRUE and if weights = varIdent(form = ~ 1 | Stratum) is specified in the model fitting, the Fisher information matrix for separate level-1 variance estimates will be returned. If separate_variances = TRUE but if the weighting structure is not specified with varIdent, or if separate_variances = FALSE, then the Fisher information matrix for the default variance components will be returned.

Examples

library(nlme)
data(Bryant2016)
Bryant2016_RML <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      data = Bryant2016)
Fisher_info(Bryant2016_RML, type = "expected")
Fisher_info(Bryant2016_RML, type = "average")

Bryant2016_RML2 <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      weights = varIdent(form = ~ 1 | treatment),
                      data = Bryant2016)
Fisher_info(Bryant2016_RML2, separate_variances = TRUE)

---

Calculates adjusted mlm effect size

Description

Estimates a standardized mean difference effect size from a fitted multi-level model, using restricted or full maximum likelihood methods with small-sample correction, as described in Pustejovsky, Hedges, & Shadish (2014).

Usage

g_mlm(
  mod,
  p_const,
  mod_denom = mod,
  r_const = NULL,
  infotype = "expected",
  separate_variances = FALSE,
  ...
)

Arguments

mod	Fitted model of class lmeStruct (estimated using nlme::lme()) or of class glsStruct (estimated using nlme::gls()), from which to estimate the numerator of the effect size.
p_const	Vector of constants for calculating numerator of effect size. Must be the same length as fixed effects in mod.
mod_denom	Fitted model of class lmeStruct (estimated using nlme::lme()) or of class glsStruct (estimated using nlme::gls()), from which to estimate the denominator of the effect size. If not otherwise specified, the same model will be used for the numerator and the denominator calculations.
r_const	Vector of constants for calculating denominator of effect size. Must be the same length as the number of variance component parameters in mod_denom.
infotype	Type of information matrix. One of "expected" (the default), "observed", or "average".
separate_variances	Logical indicating whether to incorporate separate level-1 variance components in the calculation of the effect size and standard error for models with a 'varIdent()' variance structure. If TRUE, make sure the r_const matches the parameterization of the variance component as returned by extract_varcomp(mod, separate_variances = TRUE). Default is FALSE.
...	further arguments.

Value

A list with the following components

p_beta	Numerator of effect size
r_theta	Squared denominator of effect size
delta_AB	Unadjusted (mlm) effect size estimate
nu	Estimated denominator degrees of freedom
J_nu	Biased correction factor for effect size estimate
kappa	Scaled standard error of numerator
g_AB	Corrected effect size estimate
SE_g_AB	Approximate standard error estimate
theta	Estimated variance component parameters
info_inv	Inversed information matrix

References

Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577

Examples

library(nlme)
data(Bryant2016, package = "lmeInfo")
Bryant2016_RML1 <- lme(fixed = outcome ~ treatment,
                       random = ~ 1 | school/case,
                       correlation = corAR1(0, ~ session | school/case),
                       data = Bryant2016)
Bryant2016_g1 <- g_mlm(Bryant2016_RML1, p_const = c(0,1), r_const = c(1,1,0,1),
                       infotype = "expected")
print(Bryant2016_g1)
summary(Bryant2016_g1)


Bryant2016_RML2 <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      weights = varIdent(form = ~ 1 | treatment),
                      data = Bryant2016)
Bryant_g <- g_mlm(Bryant2016_RML2, p_const = c(0,1), r_const = c(1,1,0,0,1))
Bryant_g_baseline <- g_mlm(Bryant2016_RML2,
                           p_const = c(0,1),
                           r_const = c(1,1,0,1,0),
                           separate_variances = TRUE)
Bryant_g_treatment <- g_mlm(Bryant2016_RML2,
                            p_const = c(0,1),
                            r_const = c(1,1,0,0,1),
                            separate_variances = TRUE)
print(Bryant_g)
print(Bryant_g_baseline)
print(Bryant_g_treatment)

---

Estimated sampling variance-covariance of variance component parameters.

Description

Estimate the sampling variance-covariance of variance component parameters from a fitted linear mixed effects model (lmeStruct object) or generalized least squares model (glsStruct object) using the inverse Fisher information.

Usage

varcomp_vcov(mod, type = "expected", separate_variances = FALSE)

Arguments

mod	Fitted model of class lmeStruct or glsStruct.
type	Type of information matrix. One of "expected" (the default), "observed", or "average".
separate_variances	Logical indicating whether to return the Fisher information matrix for separate level-1 variance components if using varIdent function to allow for different variances per stratum. Default is FALSE.

Value

Sampling variance-covariance matrix corresponding to variance component parameters of mod.

Examples

library(nlme)
data(Bryant2016)
Bryant2016_RML <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      data = Bryant2016)
varcomp_vcov(Bryant2016_RML, type = "expected")

Bryant2016_RML2 <- lme(fixed = outcome ~ treatment,
                      random = ~ 1 | school/case,
                      correlation = corAR1(0, ~ session | school/case),
                      weights = varIdent(form = ~ 1 | treatment),
                      data = Bryant2016)
varcomp_vcov(Bryant2016_RML2, separate_variances = TRUE)

---