WS.Corr.Mixed: Estimate within-subject correlations (reliabilities) based on...

In CorrMixed: Estimate Correlations Between Repeatedly Measured Endpoints (E.g., Reliability) Based on Linear Mixed-Effects Models

Estimate within-subject correlations (reliabilities) based on a mixed-effects model.

Description

This function allows for the estimation of the within-subject correlations using a general and flexible modeling approach that allows at the same time to capture hierarchies in the data, the presence of covariates, and the derivation of correlation estimates. Non-parametric bootstrap-based confidence intervals can be requested.

Usage

WS.Corr.Mixed(Dataset, Fixed.Part=" ", Random.Part=" ", 
Correlation=" ", Id, Time=Time, Model=1, 
Number.Bootstrap=100, Alpha=.05, Seed=1)

Arguments

Dataset	A data.frame that should consist of multiple lines per subject ('long' format).
Fixed.Part	The outcome and fixed-effect part of the mixed-effects model to be fitted. The model should be specified in agreement with the lme function requirements of the nlme package. See examples below.
Random.Part	The random-effect part of the mixed-effects model to be fitted (specified in line with the lme function requirements). See examples below.
Correlation	An optional object describing the within-group correlation structure (specified in line with the lme function requirements). See examples below.
Id	The subject indicator.
Time	The time indicator. Default Time=Time.
Model	The type of model that should be fitted. Model=1: random intercept model, Model=2: random intercept and Gaussian serial correlation, Model=3: random intercept, slope, and Gaussian serial correlation, and Model=4: random intercept + slope. Default Model=1.
Number.Bootstrap	The number of bootstrap samples to be used to estimate the Confidence Intervals around R. Default Number.Bootstrap=100. As an alternative to obtain confidence intervals, the Delta method can be used (see WS.Corr.Mixed.SAS).
Alpha	The α-level to be used in the bootstrap-based Confidence Interval for R. Default Alpha=0.05
Seed	The seed to be used in the bootstrap. Default Seed=1.

Details

Warning 1

To avoid problems with the lme function, do not specify powers directly in the function call. For example, rather than specifying Fixed.Part=ZSV ~ Time + Time**2 in the function call, first add Time**2 to the dataset (Dataset$TimeSq <- Dataset$Time ** 2) and then use the new variable name in the call: Fixed.Part=ZSV ~ Time + TimeSq

Warning 2 To avoid problems with the lme function, specify the Random.Part and Correlation arguments like e.g., Random.Part = ~ 1| Subject and Correlation=corGaus(form= ~ Time, nugget = TRUE)

not like e.g., Random.Part = ~ 1| Subject and Correlation=corGaus(form= ~ Time| Subject, nugget = TRUE)

(i.e., do not use Time| Subject)

Value

Model	The type of model that was fitted (model 1, 2, or 3.)
D	The D matrix of the fitted model.
Tau2	The τ^2 component of the fitted model. This component is only obtained when serial correlation is requested (Model 2 or 3), \varepsilon_{2} \sim N(0, τ^2 H_{i})).
Rho	The ρ component of the fitted model which determines the matrix H_{i}, ρ(|t_{ij}-t_{ik}|). This component is only obtained when serial correlation is considered (Model 2 or 3).
Sigma2	The residual variance.
AIC	The AIC value of the fitted model.
LogLik	The log likelihood value of the fitted model.
R	The estimated reliabilities.
CI.Upper	The upper bounds of the bootstrapped confidence intervals.
CI.Lower	The lower bounds of the bootstrapped confidence intervals.
Alpha	The α level used in the estimation of the confidence interval.
Coef.Fixed	The estimated fixed-effect parameters.
Std.Error.Fixed	The standard errors of the fixed-effect parameters.
Time	The time values in the dataset.
Fitted.Model	A fitted model of class lme.

Author(s)

Wim Van der Elst, Geert Molenberghs, Ralf-Dieter Hilgers, & Nicole Heussen

References

Van der Elst, W., Molenberghs, G., Hilgers, R., & Heussen, N. (2015). Estimating the reliability of repeatedly measured endpoints based on linear mixed-effects models. A tutorial. Submitted.

See Also

Explore.WS.Corr, WS.Corr.Mixed.SAS

Examples

# open data
data(Example.Data)

# Make covariates used in mixed model
Example.Data$Time2 <- Example.Data$Time**2
Example.Data$Time3 <- Example.Data$Time**3
Example.Data$Time3_log <- (Example.Data$Time**3) * (log(Example.Data$Time))

# model 1: random intercept model
Model1 <- WS.Corr.Mixed(
Fixed.Part=Outcome ~ Time2 + Time3 + Time3_log + as.factor(Cycle) 
+ as.factor(Condition), Random.Part = ~ 1|Id, 
Dataset=Example.Data, Model=1, Id="Id", Number.Bootstrap = 50, 
Seed = 12345)

  # summary of the results
summary(Model1)
  # plot the results
plot(Model1)

## Not run: time-consuming code parts
# model 2: random intercept + Gaussian serial corr
Model2 <- WS.Corr.Mixed(
Fixed.Part=Outcome ~ Time2 + Time3 + Time3_log + as.factor(Cycle) 
+ as.factor(Condition), Random.Part = ~ 1|Id, 
Correlation=corGaus(form= ~ Time, nugget = TRUE),
Dataset=Example.Data, Model=2, Id="Id", Seed = 12345)

  # summary of the results
summary(Model2)

  # plot the results
    # estimated corrs as a function of time lag (default plot)
plot(Model2)
    # estimated corrs for all pairs of time points
plot(Model2, All.Individual = T)

# model 3
Model3 <- WS.Corr.Mixed(
  Fixed.Part=Outcome ~ Time2 + Time3 + Time3_log + as.factor(Cycle) 
  + as.factor(Condition), Random.Part = ~ 1 + Time|Id, 
  Correlation=corGaus(form= ~ Time, nugget = TRUE),
  Dataset=Example.Data, Model=3, Id="Id", Seed = 12345)

  # summary of the results
summary(Model3)

  # plot the results
    # estimated corrs for all pairs of time points
plot(Model3)
    # estimated corrs as a function of time lag

## End(Not run)

CorrMixed documentation built on April 18, 2022, 5:07 p.m.