getEstimateStats function

Calculate p-Values and Confidence Intervals of Parameters for a Fitted Model

This function calculates p-values and confidence intervals (CIs) of parameters for a given model.It supports different types of CIs, including Wald CIs, likelihood-based CIs, bootstrap CIs, or all three.

getEstimateStats(
  model = NULL,
  est_in,
  p_values = TRUE,
  CI = TRUE,
  CI_type = "Wald",
  rep = NA,
  conf.level = 0.95
)

Arguments

• model: A fitted mxModel object. Specifically, this should be the mxOutput slot from the result returned by one of the estimation functions provided by this package. The default value is NULL. Providing this parameter is essential when generating likelihood-based and bootstrap confidence intervals (CIs).
• est_in: The Estimates slot from the result returned by one of the estimation functions provided by this package, which contains a dataframe with point estimates and standard errors.
• p_values: A logical flag indicating whether to calculate p-values. Default is TRUE.
• CI: A logical flag indicating whether to compute confidence intervals. Default is TRUE.
• CI_type: A string specifying the type of confidence interval to compute. Supported options include "Wald", "likelihood", "bootstrap", or "all". Default is "Wald".
• rep: An integer specifying the number of replications for bootstrap. This is applicable if CI_type is "bootstrap" or "all". Default is NA.
• conf.level: A numeric value representing the confidence level for confidence interval calculation. Default is 0.95.

Returns

An object of class StatsOutput with potential slots:

• wald: Contains a data frame with, point estimates, standard errors p-values, and Wald confidence intervals (when specified).
• likelihood: Contains a data frame with likelihood-based confidence intervals (when specified).
• bootstrap: Contains a data frame with bootstrap confidence intervals (when specified).

The content of these slots can be printed using the printTable() method for S4 objects.

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
# Load ECLS-K (2011) data
data("RMS_dat")
RMS_dat0 <- RMS_dat
# Re-baseline the data so that the estimated initial status is for the starting point of the study
baseT <- RMS_dat0$T1
RMS_dat0$T1 <- RMS_dat0$T1 - baseT
RMS_dat0$T2 <- RMS_dat0$T2 - baseT
RMS_dat0$T3 <- RMS_dat0$T3 - baseT
RMS_dat0$T4 <- RMS_dat0$T4 - baseT
RMS_dat0$T5 <- RMS_dat0$T5 - baseT
RMS_dat0$T6 <- RMS_dat0$T6 - baseT
RMS_dat0$T7 <- RMS_dat0$T7 - baseT
RMS_dat0$T8 <- RMS_dat0$T8 - baseT
RMS_dat0$T9 <- RMS_dat0$T9 - baseT
# Standardized time-invariant covariates
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)

# Fit bilinear spline latent growth curve model (fixed knots)
paraBLS_LGCM.r <- c(
  "mueta0", "mueta1", "mueta2", "knot",
  paste0("psi", c("00", "01", "02", "11", "12", "22")),
  "residuals"
  )
BLS_LGCM_r <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9, res_scale = 0.1, paramOut = TRUE, names = paraBLS_LGCM.r)
## Generate P value and Wald confidence intervals
getEstimateStats(
  est_in = BLS_LGCM_r@Estimates, CI_type = "Wald"
  )
# Fit bilinear spline latent growth curve model (random knots) with time-invariant covariates for
# mathematics development
## Define parameter names
paraBLS.TIC_LGCM.f <- c(
  "alpha0", "alpha1", "alpha2", "alphag",
  paste0("psi", c("00", "01", "02", "0g", "11", "12", "1g", "22", "2g", "gg")), "residuals",
  paste0("beta1", c(0:2, "g")), paste0("beta2", c(0:2, "g")), paste0("mux", 1:2),
  paste0("phi", c("11", "12", "22")), "mueta0", "mueta1", "mueta2", "mu_knot"
  )
## Fit the model
BLS_LGCM.TIC_f <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = TRUE, records = 1:9,
  growth_TIC = c("ex1", "ex2"), res_scale = 0.1, paramOut = TRUE, names = paraBLS.TIC_LGCM.f
  )
## Change optimizer to "SLSQP" for getting likelihood-based confidence interval
mxOption(model = NULL, key = "Default optimizer", "SLSQP", reset = FALSE)
## Generate P value and all three types of confidence intervals
getEstimateStats(
  model = BLS_LGCM.TIC_f@mxOutput, est_in = BLS_LGCM.TIC_f@Estimates, CI_type = "all", rep = 1000
  )

References

• Casella, G. & Berger, R.L. (2002). Statistical Inference (2nd ed.). Duxbury Press.
• Madansky, A. (1965). Approximate Confidence Limits for the Reliability of Series and Parallel Systems. Technometrics, 7(4), 495-503. Taylor & Francis, Ltd. https://www.jstor.org/stable/1266390
• Matthews, D. E. (1988). Likelihood-Based Confidence Intervals for Functions of Many Parameters. Biometrika, 75(1), 139-144. Oxford University Press. https://www.jstor.org/stable/2336444
• Efron, B. & Tibshirani, R. J. (1994). An Introduction to the Bootstrap. CRC press.