S4 Class for estimated factor scores and their standard errors.

Description

S4 Class for the output structure for the getIndFS() function.

Slots

scores_est

A matrix of estimated factor scores.

scores_se

A matrix of standard errors of estimated factor scores.

S4 Class for kappa statistic with confidence interval and judgment.

Description

S4 Class for the output structure for the getLatentKappa() function.

Slots

kappa_value

A character vector for the kappa statistic with 95% CI.

judgment

A character vector for the judgement for agreement.

S4 Generic for summarizing an optimized MxModel.

Description

Generic function for printing model summary of MxModel object.

Usage

ModelSummary(object)

Arguments

Value

Invisibly returns the summary of the MxModel object. Called primarily for its side effect of printing the model summary.

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
data("RMS_dat")
RMS_dat0 <- RMS_dat
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
BLS_LGCM <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9
)
ModelSummary(BLS_LGCM)

S4 Method for summarizing an optimized MxModel.

Description

Method for printing model summary of MxModel object.

Usage

## S4 method for signature 'myMxOutput'
ModelSummary(object)

Arguments

Value

Invisibly returns the summary of the MxModel object. Called primarily for its side effect of printing the model summary.

ECLS-K (2011) Sample Dataset for Demonstration

Description

A sample dataset extracted from the public-use Early Childhood Longitudinal Study, Kindergarten Class of 2010-11 (ECLS-K:2011) collected by the National Center for Education Statistics (NCES). This dataset is NOT a posting of the original data, and it has been processed and formatted for use in demonstration purposes within this package. For access to the original data, please visit the NCES data products page at https://nces.ed.gov/ecls/dataproducts.asp.

Usage

RMS_dat

Format

A data frame with 500 rows and 49 variables:

ID

Identification number.

R1, R2, R3, R4, R5, R6, R7, R8, R9

Reading scores from 9 study waves.

M1, M2, M3, M4, M5, M6, M7, M8, M9

Math scores from 9 study waves.

S2, S3, S4, S5, S6, S7, S8, S9

Science scores from 8 study waves (starting from the second study wave).

T1, T2, T3, T4, T5, T6, T7, T8, T9

Children's age-in-month at 9 study waves.

SEX

Sex of the child.

RACE

Race of the child.

LOCALE

Locale of the child's school.

INCOME

Family income.

SCHOOL_TYPE

Type of the child's school.

Approach_to_Learning

Teacher's rating on the child's approach to learning.

Self_control

Teacher's rating on the child's self-control.

Interpersonal

Teacher's rating on the child's interpersonal skills.

External_prob_Behavior

Teacher's rating on the child's external problem behaviors.

Internal_prob_Behavior

Teacher's rating on the child's internal problem behaviors.

Attention_focus

Teacher's rating on the child's attention focus.

Inhibitory_Ctrl

Teacher's rating on the child's inhibitory control.

EDU

Highest education level between the child's parents.

Details

The ECLS-K:2011 offers a comprehensive and detailed set of information about children's early life experiences, focusing on children's health, development, education, and experiences in the years leading up to kindergarten.

The sample dataset included in this package is used for demonstrating the functionality of the package's functions and it does not include survey weights. In real analysis, the complex survey weights provided by NCES should be utilized appropriately, for instance, as done in R packages such as lavaan.survey or EdSurvey if not using SEM.

Please note that this data must not be used to attempt to identify respondents. For detailed documentation and proper usage of the ECLS-K:2011 data, please refer to the original source at the National Center for Education Statistics (NCES) website: https://nces.ed.gov/.

Source

https://nces.ed.gov/ecls/dataproducts.asp

S4 Class for p values and confidence intervals (when specified).

Description

S4 Class for the output structure for the getEstimateStats() function.

Slots

wald

A data frame for p values and Wald confidence intervals (when specified).

likelihood

A data frame for Likelihood confidence intervals (when specified).

bootstrap

A data frame for Bootstrap confidence intervals (when specified).

S4 Class for displaying figures

Description

S4 Class to hold the figures output from the getFigure function.

Slots

figures

A list of lists containing figures for each specified sub_model and y_model (when applicable).

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

Description

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.

Usage

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

Arguments

Value

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.

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.

See Also

getLGCM, getIndFS, getPosterior

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)
BLS_LGCM_r <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9, paramOut = TRUE)
## Generate P value and Wald confidence intervals
getEstimateStats(
  est_in = BLS_LGCM_r@Estimates, CI_type = "Wald"
  )

## Not run: 
# Fit bilinear spline latent growth curve model (random knots) with time-invariant covariates for
# mathematics development
## Fit the model
set.seed(20191029)
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"), tries = 20, paramOut = TRUE
  )
## 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 = 20
  )

## End(Not run)

Generate Visualization for Fitted Model

Description

This function generates visualizations for the output of a fitted model. When a Latent Growth Curve Model (LGCM) is fitted for the longitudinal process, it provides (class-specific) estimated growth status with 95% confidence intervals. When a Latent Change Score Model (LCSM) is fitted for the longitudinal process, it provides (class-specific) estimated growth rate with 95% confidence intervals and change from baseline with 95% confidence intervals. These visualizations are particularly useful for understanding the results and trajectories of different classes or groups within the model.

Usage

getFigure(
  model,
  nClass = NULL,
  cluster_TIC = NULL,
  grp_var = NULL,
  sub_Model,
  y_var,
  curveFun,
  y_model = NULL,
  t_var,
  records,
  m_var = NULL,
  x_type = NULL,
  x_var = NULL,
  xstarts,
  xlab = "Time",
  outcome = "Process"
)

Arguments

Value

An object of class figOutput containing a slot named figures. This slot holds a ggplot object or a list of ggplot objects, each representing a figure for the fitted model. If the figures slot contains a list of ggplot objects, individual figures can be visualized using the show() function.

See Also

getLGCM, getLCSM, getTVCmodel, getMGM, getMediation, getMGroup, getMIX

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
xstarts <- mean(baseT)


# Plot single group LGCM model
set.seed(20191029)
BLS_LGCM1 <- getLGCM(dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS",
                     intrinsic = FALSE, records = 1:9)
Figure1 <- getFigure(
  model = BLS_LGCM1@mxOutput, nClass = NULL, cluster_TIC = NULL, sub_Model = "LGCM",
  y_var = "M", curveFun = "BLS", y_model = "LGCM", t_var = "T", records = 1:9,
  m_var = NULL, x_var = NULL, x_type = NULL, xstarts = xstarts, xlab = "Month",
  outcome = "Mathematics"
)
show(Figure1)
# Plot mixture LGCM model
BLS_LGCM2 <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.45, 0.55), sub_Model = "LGCM",
  cluster_TIC = NULL, y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE
)
Figure2 <- getFigure(
  model = BLS_LGCM2@mxOutput, nClass = 2, cluster_TIC = NULL, sub_Model = "LGCM",
  y_var = "M", curveFun = "BLS", y_model = "LGCM", t_var = "T", records = 1:9,
  m_var = NULL, x_var = NULL, x_type = NULL, xstarts = xstarts, xlab = "Month",
  outcome = "Mathematics"
)
show(Figure2)

Derive Individual Factor Scores for Each Latent Variable Included in Model

Description

This function computes individual factor scores for each latent variable in a given model. It supports three types of factor scores: maximum likelihood, weighted maximum likelihood, and regression.

Usage

getIndFS(model, FS_type = "Regression")

Arguments

Value

An object of class FSOutput with two slots:

• scores_est: Contains the factor score estimates.

• scores_se: Contains the standard errors of the factor score estimates.

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

References

• Estabrook, R. & Neale, M. C. (2013). A Comparison of Factor Score Estimation Methods in the Presence of Missing Data: Reliability and an Application to Nicotine Dependence. Multivariate Behavioral Research, 48, 1-27. doi:10.1080/00273171.2012.730072

• Priestley, M. & Subba Rao, T. (1975). The Estimation of Factor Scores and Kalman Filtering For Discrete Parameter Stationary Processes. International Journal of Control, 21, 971-975. doi:10.1080/00207177508922050

See Also

getEstimateStats

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)
LIN_LGCM <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "linear",
  intrinsic = FALSE, records = 1:9, growth_TIC = NULL
)
getIndFS(model = LIN_LGCM@mxOutput, FS_type = "Regression")
# Fit bilinear spline latent growth curve model (random knots) with time-invariant covariates for
# mathematics development
## Fit the model
set.seed(20191029)
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"),
                          tries = 20)
getIndFS(model = BLS_LGCM.TIC_f@mxOutput, FS_type = "Regression")

Fit a Latent Change Score Model with a Time-invariant Covariate (If Any)

Description

This function fits a latent change score model with or without time-invariant covariates to the provided data. It manages model setup, optimization, and if requested, outputs parameter estimates and standard errors.

Usage

getLCSM(
  dat,
  t_var,
  y_var,
  curveFun,
  intrinsic = TRUE,
  records,
  growth_TIC = NULL,
  starts = NULL,
  res_scale = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted latent change score model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R. A. (2023). Estimating Rate of Change for Nonlinear Trajectories in the Framework of Individual Measurement Occasions: A New Perspective on Growth Curves. Behavior Research Methods, 56(3), 1349-1375. doi:10.3758/s13428-023-02097-2

• Liu, J. (2022). "Jenss–Bayley Latent Change Score Model With Individual Ratio of the Growth Acceleration in the Framework of Individual Measurement Occasions." Journal of Educational and Behavioral Statistics, 47(5), 507–543. doi:10.3102/10769986221099919

• Grimm, K. J., Zhang, Z., Hamagami, F., & Mazzocco, M. (2013). "Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories." Multivariate Behavioral Research, 48(1), 117-143. doi:10.1080/00273171.2012.755111

See Also

getLGCM, getTVCmodel, getFigure

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$T1 - baseT)/12
RMS_dat0$T2 <- (RMS_dat0$T2 - baseT)/12
RMS_dat0$T3 <- (RMS_dat0$T3 - baseT)/12
RMS_dat0$T4 <- (RMS_dat0$T4 - baseT)/12
RMS_dat0$T5 <- (RMS_dat0$T5 - baseT)/12
RMS_dat0$T6 <- (RMS_dat0$T6 - baseT)/12
RMS_dat0$T7 <- (RMS_dat0$T7 - baseT)/12
RMS_dat0$T8 <- (RMS_dat0$T8 - baseT)/12
RMS_dat0$T9 <- (RMS_dat0$T9 - baseT)/12
# Standardized time-invariant covariates
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)


# Fit nonparametric change score model for reading development
## Fit model
NonP_LCSM <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "nonparametric",
  intrinsic = FALSE, records = 1:9
  )

Fit a Latent Growth Curve Model with Time-invariant Covariate (If Any)

Description

This function fits a latent growth curve model with or without time-invariant covariates to the provided data. It manages model setup, optimization, and if requested, outputs parameter estimates and standard errors.

Usage

getLGCM(
  dat,
  t_var,
  y_var,
  curveFun,
  intrinsic = TRUE,
  records,
  growth_TIC = NULL,
  starts = NULL,
  res_scale = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted latent growth curve model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., Perera, R. A., Kang, L., Kirkpatrick, R. M., & Sabo, R. T. (2021). "Obtaining Interpretable Parameters from Reparameterizing Longitudinal Models: Transformation Matrices between Growth Factors in Two Parameter Spaces". Journal of Educational and Behavioral Statistics. doi:10.3102/10769986211052009

• Sterba, S. K. (2014). "Fitting Nonlinear Latent Growth Curve Models With Individually Varying Time Points". Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 630-647. doi:10.1080/10705511.2014.919828

See Also

getLCSM, getTVCmodel, getFigure

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)
BLS_LGCM_r <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "bilinear spline",
  intrinsic = FALSE, records = 1:9, growth_TIC = NULL
)
# Fit bilinear spline latent growth curve model (random knots) with
# time-invariant covariates for mathematics development
## Fit the model
set.seed(20191029)
BLS_LGCM.TIC_f <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "bilinear spline",
  intrinsic = TRUE, records = 1:9, growth_TIC = c("ex1", "ex2"),
  tries = 20, paramOut = TRUE
)
## Output point estimate and standard errors
printTable(BLS_LGCM.TIC_f)

Perform Bootstrap Likelihood Ratio Test for Comparing Full and Reduced Models

Description

This function performs the likelihood ratio test (LRT) to compare a full model (an intrinsically nonlinear longitudinal model) with a corresponding parsimonious alternative (a non-intrinsically nonlinear longitudinal model). It also provides an option to perform bootstrapping for the comparison.

Usage

getLRT(full, reduced, boot = FALSE, rep = NA)

Arguments

Value

A data frame containing the number of free parameters, estimated likelihood (-2ll), degrees of freedom, differences in log-likelihood and degrees of freedom, p-values, AIC, and BIC for both the full and reduced models.

See Also

getSummary

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


# Fit bilinear spline growth model with random knot (intrinsically nonlinear model)
BLS_LGCM_f <- getLGCM(dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "bilinear spline",
                      intrinsic = TRUE, records = 1:9)
# Fit bilinear spline growth model with fix knot (non-intrinsically nonlinear model)
BLS_LGCM_r <- getLGCM(dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "bilinear spline",
                      intrinsic = FALSE, records = 1:9)
# Likelihood ratio test
getLRT(full = BLS_LGCM_f@mxOutput, reduced = BLS_LGCM_r@mxOutput, boot = FALSE, rep = NA)

Compute Latent Kappa Coefficient for Agreement between Two Latent Label Sets

Description

This function calculates the latent kappa, a measure of agreement between two sets of latent categorical labels. It also computes the confidence interval and provides a qualitative interpretation of the agreement level.

Usage

getLatentKappa(label1, label2, conf.level = 0.95)

Arguments

Value

An object of class KappaOutput with the following slots:

• kappa_value: A string representing the kappa statistic along with its confidence interval.

• judgment: A string describing the level of agreement, such as "Perfect Agreement", "Slight Agreement", etc.

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

References

• Dumenci, L. (2011). The Psychometric Latent Agreement Model (PLAM) for Discrete Latent Variables Measured by Multiple Items. Organizational Research Methods, 14(1), 91-115. SAGE Publications. doi:10.1177/1094428110374649

• Landis, J., & Koch, G. (1977). The Measurement of Observer Agreement for Categorical Data. Biometrics, 33(1), 159-174. doi:10.2307/2529310

• Agresti, A. (2012). Models for Matched Pairs. In Categorical Data Analysis (pp. 413-454). Wiley.

See Also

getPosterior, getMIX

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
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$T9 - baseT
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)
RMS_dat0$gx1 <- scale(RMS_dat0$INCOME)
RMS_dat0$gx2 <- scale(RMS_dat0$EDU)

## Fit a growth mixture model with no TICs
set.seed(20191029)
MIX_BLS_LGCM_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.30, 0.40, 0.30), sub_Model = "LGCM",
  cluster_TIC = NULL, y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE, growth_TIC = NULL, tries = 10
)
## Membership of each individual from growth mixture model with no TICs
label1 <- getPosterior(
  model = MIX_BLS_LGCM_r@mxOutput, nClass = 3, label = FALSE, cluster_TIC = NULL
)
set.seed(20191029)
## Fit a growth mixture model with growth TICs and cluster TICs
MIX_BLS_LGCM.TIC_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.33, 0.34, 0.33), sub_Model = "LGCM",
  cluster_TIC = c("gx1", "gx2"), y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE,
  growth_TIC = c("ex1", "ex2"), tries = 10
)
## Membership of each individual from growth mixture model with growth TICs and cluster TICs
label2 <- getPosterior(
  model = MIX_BLS_LGCM.TIC_r@mxOutput, nClass = 3, label = FALSE,
  cluster_TIC = c("gx1", "gx2")
)
## Calculate the agreement between two sets of membership labels
getLatentKappa(label1 = label1@membership, label2 = label2@membership)

Fit a Multivariate Latent Growth Curve Model or Multivariate Latent Change Score Model

Description

This function fits a multivariate latent growth curve model or a multivariate latent change score model with the provided data. It manages model setup, optimization, and if requested, outputs parameter estimates and standard errors.

Usage

getMGM(
  dat,
  t_var,
  y_var,
  curveFun,
  intrinsic = TRUE,
  records,
  y_model,
  starts = NULL,
  res_scale = NULL,
  res_cor = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted multivariate latent growth curve model or a multivariate latent change score model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R. A. (2021). "Estimating Knots and Their Association in Parallel Bilinear Spline Growth Curve Models in the Framework of Individual Measurement Occasions," Psychological Methods, 27(5), 703-729. doi:10.1037/met0000309

• Blozis, S. A. (2004). "Structured Latent Curve Models for the Study of Change in Multivariate Repeated Measures," Psychological Methods, 9(3), 334-353. doi:10.1037/1082-989X.9.3.334

See Also

getLGCM, getMGroup, getMIX, getFigure

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


# Fit linear multivariate latent growth curve model
LIN_PLGCM_f <- getMGM(
  dat = RMS_dat0, t_var = c("T", "T"), y_var = c("R", "M"), curveFun = "LIN",
  intrinsic = FALSE, records = list(1:9, 1:9), y_model = "LGCM"
  )
# Fit bilinear spline multivariate latent growth curve model (random knots)
## Fit model
set.seed(20191029)
BLS_PLGCM_f <- getMGM(
  dat = RMS_dat0, t_var = c("T", "T"), y_var = c("R", "M"), curveFun = "BLS", intrinsic = TRUE,
  records = list(1:9, 1:9), y_model = "LGCM",
  tries = 20, paramOut = TRUE
  )
printTable(BLS_PLGCM_f)

Fit a Longitudinal Multiple Group Model

Description

This function fits a longitudinal multiple group model based on the specified sub-model. Supported submodels include:

• Latent growth curve models,

• Latent change score models,

• Latent growth curve models or latent change score models with a time-varying covariate,

• Multivariate latent growth curve models or multivariate latent change score models,

• Longitudinal mediation models.

For the first three submodels, time-invariant covariates are allowed.

Usage

getMGroup(
  dat,
  grp_var,
  sub_Model,
  t_var,
  records,
  y_var,
  curveFun,
  intrinsic = NULL,
  y_model = NULL,
  m_var = NULL,
  x_type = NULL,
  x_var = NULL,
  TVC = NULL,
  decompose = NULL,
  growth_TIC = NULL,
  starts = NULL,
  res_scale = NULL,
  res_cor = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted longitudinal multiple group model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R. A. (2023). Estimating Rate of Change for Nonlinear Trajectories in the Framework of Individual Measurement Occasions: A New Perspective on Growth Curves. Behavior Research Methods, 56(3), 1349-1375. doi:10.3758/s13428-023-02097-2

See Also

getLGCM, getLCSM, getMIX, getFigure

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
data("RMS_dat")
# Re-baseline the data so that the estimated initial status is for the starting point of the study
RMS_dat0 <- RMS_dat
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$T9 - baseT
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)

# Fit longitudinal multiple group model of bilinear spline functional form with fixed knot
MGroup_BLS_LGCM.TIC_f <-  getMGroup(
  dat = RMS_dat0, grp_var = "SEX", sub_Model = "LGCM", y_var = "M", t_var = "T",
  records = 1:9, curveFun = "BLS", intrinsic = FALSE
)

# Fit longitudinal multiple group model of bilinear spline functional form with random knot
set.seed(20191029)
MGroup_BLS_LGCM.TIC_f <-  getMGroup(
  dat = RMS_dat0, grp_var = "SEX", sub_Model = "LGCM", y_var = "M", t_var = "T",
  records = 1:9, curveFun = "BLS", intrinsic = TRUE,
  growth_TIC = c("ex1", "ex2"), tries = 10, paramOut = TRUE
)
printTable(MGroup_BLS_LGCM.TIC_f)

Fit a Longitudinal Mixture Model

Description

This function fits a longitudinal mixture model based on the specified sub-model. Supported submodels include:

• Latent growth curve models,

• Latent change score models,

• Latent growth curve models or latent change score models with a time-varying covariate,

• Multivariate latent growth curve models or multivariate latent change score models,

• Longitudinal mediation models.

Time-invariant covariates are allowed for the first three submodels.

Usage

getMIX(
  dat,
  prop_starts,
  sub_Model,
  cluster_TIC = NULL,
  t_var,
  records,
  y_var,
  curveFun,
  intrinsic = NULL,
  y_model = NULL,
  m_var = NULL,
  x_type = NULL,
  x_var = NULL,
  TVC = NULL,
  decompose = NULL,
  growth_TIC = NULL,
  starts = NULL,
  res_scale = NULL,
  res_cor = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted longitudinal mixture model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R. A. (2022). Extending Mixture of Experts Model to Investigate Heterogeneity of Trajectories: When, Where and How to Add Which Covariates. Psychological Methods, 28(1), 152-178. doi:10.1037/met0000436

• Liu, J., & Perera, R. A. (2022). Extending Growth Mixture Model to Assess Heterogeneity in Joint Development with Piecewise Linear Trajectories in the Framework of Individual Measurement Occasions. Psychological Methods, 28(5), 1029-1051. doi:10.1037/met0000500

• Liu, J., & Perera, R. A. (2023). Estimating Rate of Change for Nonlinear Trajectories in the Framework of Individual Measurement Occasions: A New Perspective on Growth Curves. Behavior Research Methods, 56(3), 1349-1375. doi:10.3758/s13428-023-02097-2

• Liu, J. (2023). Further Exploration of the Effects of Time-varying Covariate in Growth Mixture Models with Nonlinear Trajectories. Behavior Research Methods, 56(4), 2804-2827. doi:10.3758/s13428-023-02183-5

See Also

getLGCM, getLCSM, getMGroup, getFigure

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
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$T9 - baseT
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)
RMS_dat0$gx1 <- scale(RMS_dat0$INCOME)
RMS_dat0$gx2 <- scale(RMS_dat0$EDU)

# Fit longitudinal mixture group model of bilinear spline functional form with fixed knot
# (2 classes)
MIX_BLS_LGCM.TIC_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.45, 0.55), sub_Model = "LGCM",
  cluster_TIC = NULL, y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE
  )
# Fit longitudinal mixture group model of bilinear spline functional form with fixed knot
# (3 classes)
set.seed(20191029)
MIX_BLS_LGCM.TIC_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.33, 0.34, 0.33), sub_Model = "LGCM",
  cluster_TIC = c("gx1", "gx2"), y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE,
  growth_TIC = c("ex1", "ex2"), tries = 10, paramOut = TRUE
)
printTable(MIX_BLS_LGCM.TIC_r)

Fit a Longitudinal Mediation Model

Description

This function fits a longitudinal mediation model to the provided data. It manages model setup, optimization, and if requested, outputs parameter estimates and standard errors.

Usage

getMediation(
  dat,
  t_var,
  y_var,
  m_var,
  x_type,
  x_var,
  curveFun,
  records,
  starts = NULL,
  res_scale = NULL,
  res_cor = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted longitudinal mediation model. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R.A. (2022). Assessing Mediational Processes Using Piecewise Linear Growth Curve Models with Individual Measurement Occasions. Behavior Research Methods, 55(6), 3218-3240. doi:10.3758/s13428-022-01940-2

• MacKinnon, D. P. (2008). Introduction to Statistical Mediation Analysis. Taylor & Francis Group/Lawrence Erlbaum Associates.

• Cheong, J., Mackinnon, D. P., & Khoo, S. T. (2003). Investigation of Mediational Processes Using Parallel Process Latent Growth Curve Modeling. Structural equation modeling: a multidisciplinary journal, 10(2), 238-262. doi:10.1207/S15328007SEM1002_5

• Soest, T., & Hagtvet, K. A. (2011). Mediation Analysis in a Latent Growth Curve Modeling Framework. Structural equation modeling: a multidisciplinary journal, 18(2), 289-314. doi:10.1080/10705511.2011.557344

See Also

getLGCM, getTVCmodel, getFigure

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)


# Example 1: Baseline predictor, linear functional form
## Fit model
set.seed(20191029)
Med2_LGCM_LIN <- getMediation(
  dat = RMS_dat0, t_var = rep("T", 2), y_var = "M", m_var = "R", x_type = "baseline",
  x_var = "ex1", curveFun = "LIN", records = list(1:9, 1:9)
  )

# Example 2: Longitudinal predictor, bilinear spline functional form
## Fit model
set.seed(20191029)
Med3_LGCM_BLS <- getMediation(
  dat = RMS_dat0, t_var = rep("T", 3), y_var = "S", m_var = "M", x_type = "longitudinal",
  x_var = "R", curveFun = "bilinear spline", records = list(2:9, 1:9, 1:9),
  tries = 10, paramOut = TRUE
  )
printTable(Med3_LGCM_BLS)

Compute Posterior Probabilities, Cluster Assignments, and Model Entropy for a Longitudinal Mixture Model

Description

This function computes posterior probabilities, cluster assignments, and model entropy for a given mixture model with a predefined number of classes. If the true labels are available, it can also compute the model accuracy.

Usage

getPosterior(model, nClass, label = FALSE, cluster_TIC = NULL)

Arguments

Value

An object of class postOutput. Depending on the label argument, the object may contain the following slots:

• prob: A matrix of posterior probabilities.

• membership: A vector indicating class membership based on maximum posterior probability.

• entropy: The entropy of the model, a measure of uncertainty in class assignment.

• accuracy (optional): If label = TRUE, the model's accuracy based on true labels.

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

References

• Peugh, J., & Fan, X. (2015). Enumeration Index Performance in Generalized Growth Mixture Models: A Monte Carlo Test of Muthén's (2003) Hypothesis. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 115-131. Routledge. doi:10.1080/10705511.2014.919823

• Lubke, G., & Muthén, B.O. (2007). Performance of Factor Mixture Models as a Function of Model Size, Covariate Effects, and Class-Specific Parameters. Structural Equation Modeling: A Multidisciplinary Journal, 14(1), 26-47. Routledge. doi:10.1080/10705510709336735

See Also

getMIX, getLatentKappa

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
data("RMS_dat")
# Re-baseline the data so that the estimated initial status is for the starting point of the study
RMS_dat0 <- RMS_dat
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$T9 - baseT
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)
RMS_dat0$gx1 <- scale(RMS_dat0$INCOME)
RMS_dat0$gx2 <- scale(RMS_dat0$EDU)

# Fit longitudinal mixture group model of bilinear spline functional form with fixed knot but no
# cluster TICs or growth TICs
set.seed(20191029)
MIX_BLS_LGCM_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.30, 0.40, 0.30), sub_Model = "LGCM",
  cluster_TIC = NULL, y_var = "M", t_var = "T", records = 1:9, curveFun = "BLS",
  intrinsic = FALSE, growth_TIC = NULL, tries = 10
)
label1 <- getPosterior(
  model = MIX_BLS_LGCM_r@mxOutput, nClass = 3, label = FALSE, cluster_TIC = NULL
)
# Fit longitudinal mixture group model of bilinear spline functional form with fixed knot, cluster
# TICs, and growth TICs
set.seed(20191029)
MIX_BLS_LGCM.TIC_r <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.33, 0.34, 0.33), sub_Model = "LGCM",
  cluster_TIC = c("gx1", "gx2"), y_var = "M", t_var = "T", records = 1:9,
  curveFun = "BLS", intrinsic = FALSE,
  growth_TIC = c("ex1", "ex2"), tries = 10
)
label2 <- getPosterior(
  model = MIX_BLS_LGCM.TIC_r@mxOutput, nClass = 3, label = FALSE, cluster_TIC = c("gx1", "gx2")
)

Summarize Model Fit Statistics for Fitted Models

Description

This function summarizes the model fit statistics for a list of fitted models. The summary includes the number of parameters, estimated likelihood (-2ll), AIC, BIC, and other relevant statistics.

Usage

getSummary(model_list, HetModels = FALSE)

Arguments

Value

A data frame summarizing model fit statistics (number of parameters, estimated likelihood, AIC, BIC, etc.) for each model.

See Also

getLGCM, getMIX, getMGroup

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

# Fit bilinear spline growth model with fix knot
## Single group model
BLS_LGCM1 <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9
  )
getSummary(model_list = list(BLS_LGCM1@mxOutput), HetModels = FALSE)
## Mixture model with two latent classes
set.seed(20191029)
BLS_LGCM2 <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.45, 0.55), sub_Model = "LGCM", cluster_TIC = NULL,
  y_var = "M", t_var = "T", records = 1:9, curveFun = "BLS", intrinsic = FALSE,
  growth_TIC = NULL, tries = 10
  )
## Mixture model with three latent classes
set.seed(20191029)
BLS_LGCM3 <-  getMIX(
  dat = RMS_dat0, prop_starts = c(0.30, 0.40, 0.30), sub_Model = "LGCM", cluster_TIC = NULL,
  y_var = "M", t_var = "T", records = 1:9, curveFun = "BLS", intrinsic = FALSE,
  growth_TIC = NULL, tries = 10
  )

getSummary(model_list = list(BLS_LGCM1@mxOutput, BLS_LGCM2@mxOutput, BLS_LGCM3@mxOutput),
  HetModels = TRUE)

Fit a Latent Growth Curve Model or Latent Change Score Model with Time-varying and Time-invariant Covariates

Description

This function fits a latent growth curve model or latent change score model with a time-varying covariate and potential time-invariant covariates to the provided data. It manages model setup, optimization, and if requested, outputs parameter estimates and standard errors.

Usage

getTVCmodel(
  dat,
  t_var,
  y_var,
  curveFun,
  intrinsic = TRUE,
  records,
  y_model,
  TVC,
  decompose,
  growth_TIC = NULL,
  starts = NULL,
  res_scale = NULL,
  res_cor = NULL,
  tries = NULL,
  OKStatus = 0,
  jitterD = "runif",
  loc = 1,
  scale = 0.25,
  paramOut = FALSE,
  names = NULL
)

Arguments

Value

An object of class myMxOutput. Depending on the paramOut argument, the object may contain the following slots:

• mxOutput: This slot contains the fitted latent growth curve model or latent change score model with a time-varying covariate. A summary of this model can be obtained using the ModelSummary() function.

• Estimates (optional): If paramOut = TRUE, a data frame with parameter estimates and standard errors. The content of this slot can be printed using the printTable() method for S4 objects.

References

• Liu, J., & Perera, R. A. (2023). Estimating Rate of Change for Nonlinear Trajectories in the Framework of Individual Measurement Occasions: A New Perspective on Growth Curves. Behavior Research Methods, 56(3), 1349-1375. doi:10.3758/s13428-023-02097-2

• Liu, J. (2025). Decomposing Impact on Longitudinal Outcome of Time-varying Covariate into Baseline Effect and Temporal Effect. Journal of Educational and Behavioral Statistics, 50(5), 765-805. doi:10.3102/10769986241263975

See Also

getLGCM, getLCSM, getFigure

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
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$T1 - baseT)/12
RMS_dat0$T2 <- (RMS_dat0$T2 - baseT)/12
RMS_dat0$T3 <- (RMS_dat0$T3 - baseT)/12
RMS_dat0$T4 <- (RMS_dat0$T4 - baseT)/12
RMS_dat0$T5 <- (RMS_dat0$T5 - baseT)/12
RMS_dat0$T6 <- (RMS_dat0$T6 - baseT)/12
RMS_dat0$T7 <- (RMS_dat0$T7 - baseT)/12
RMS_dat0$T8 <- (RMS_dat0$T8 - baseT)/12
RMS_dat0$T9 <- (RMS_dat0$T9 - baseT)/12
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)

# Standardize reading ability over time with its baseline value
BL_mean <- mean(RMS_dat0[, "R1"])
BL_var <- var(RMS_dat0[, "R1"])
RMS_dat0$Rs1 <- (RMS_dat0$R1 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs2 <- (RMS_dat0$R2 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs3 <- (RMS_dat0$R3 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs4 <- (RMS_dat0$R4 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs5 <- (RMS_dat0$R5 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs6 <- (RMS_dat0$R6 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs7 <- (RMS_dat0$R7 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs8 <- (RMS_dat0$R8 - BL_mean)/sqrt(BL_var)
RMS_dat0$Rs9 <- (RMS_dat0$R9 - BL_mean)/sqrt(BL_var)


# Fit bilinear spline latent growth curve model (fixed knot) with a time-varying
# reading ability for mathematics development
BLS_TVC_LGCM1 <- getTVCmodel(
 dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
 records = 1:9, y_model = "LGCM", TVC = "Rs", decompose = 0, growth_TIC = NULL
 )

# Fit negative exponential latent growth curve model (random ratio) with a
# decomposed time-varying reading ability and time-invariant covariates for
# mathematics development
set.seed(20191029)
EXP_TVCslp_LGCM3.f <- getTVCmodel(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "EXP", intrinsic = TRUE,
  records = 1:9, y_model = "LGCM", TVC = "Rs", decompose = 1,
  growth_TIC = c("ex1", "ex2"),
  tries = 20, paramOut = TRUE
)
printTable(EXP_TVCslp_LGCM3.f)

S4 Class for optimized MxModel and point estimates with standard errors (when applicable)

Description

S4 Class for the output structure for estimate functions.

Slots

mxOutput

An object of class "MxModel".

Estimates

A data frame of estimates.

S4 Class for posterior probabilities, membership, entropy, and accuracy (when applicable)

Description

S4 Class for the output structure for the getPosterior() function.

Slots

prob

A matrix of posterior probabilities.

membership

A numeric vector for membership.

entropy

A numeric value for entropy.

accuracy

A numeric value for accuracy.

S4 Generic for displaying output in a table format.

Description

Generic function for printing output as tables.

Usage

printTable(object)

Arguments

Value

Called primarily for its side effect of printing formatted output. Returns the object invisibly.

Examples

mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
data("RMS_dat")
RMS_dat0 <- RMS_dat
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
BLS_LGCM <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9, paramOut = TRUE
)
printTable(BLS_LGCM)

S4 Method for printing estimated factor scores and their standard errors

Description

Method for printing estimated factor scores and their standard errors.

Usage

## S4 method for signature 'FSOutput'
printTable(object)

Arguments

Value

Called for its side effect of printing factor scores and their standard errors. Returns the object invisibly.

S4 Method for printing kappa statistic with 95% CI and judgement for agreement.

Description

Method for printing kappa statistic with 95% CI and judgement for agreement.

Usage

## S4 method for signature 'KappaOutput'
printTable(object)

Arguments

Value

Called for its side effect of printing kappa statistic with confidence interval and agreement judgment. Returns the object invisibly.

S4 Method for printing p values and confidence intervals (when applicable)

Description

Method for printing p values and confidence intervals.

Usage

## S4 method for signature 'StatsOutput'
printTable(object)

Arguments

Value

Called for its side effect of printing p values and confidence intervals. Returns the object invisibly.

S4 Method for printing point estimates with standard errors

Description

Method for printing point estimates and standard errors.

Usage

## S4 method for signature 'myMxOutput'
printTable(object)

Arguments

Value

Called for its side effect of printing point estimates and standard errors. Returns the object invisibly.

S4 Method for printing posterior probabilities, membership, entropy, and accuracy.

Description

Method for printing posterior probabilities, membership, entropy, and accuracy.

Usage

## S4 method for signature 'postOutput'
printTable(object)

Arguments

Value

Called for its side effect of printing posterior probabilities, membership, entropy, and accuracy. Returns the object invisibly.

S4 Method for displaying figures.

Description

Method to display a summary of the figOutput object when printed.

Usage

## S4 method for signature 'figOutput'
show(object)

Arguments

Value

Called for its side effect of displaying figures. Returns the object invisibly.