qcpm {qcpm}

QC-PM: Quantile Composite-based Path Modeling

Description

qcpm estimates path model parameters by quantile composite-based path modeling approach.

Usage

qcpm(
  model,
  data,
  scheme = "factorial",
  tau = NULL,
  fix.quantile = FALSE,
  qcorr = FALSE,
  tol = 1e-05,
  maxiter = 100
)

Arguments

model

A description of the user-specified model. The model is described using the lavaan sintax. Structural and measurement model are defined enclosed between double quotes. The directional link between constructs is defined by using the tilde ("~") operator. On the left-hand side of the operator there is the dependent construct and on the right-hand side the explanatory constructs, separated by the ("+") operator. As for the outer model, constructs are defined by listing their corresponding MVs after the operator (“=~”) if Mode A is the choice for computing the outer weights, or the operator(“<~”) if Mode B is chosen. On the left-hand side of the operator, there is the construct and on the right-hand side the MVs separated by the ("+") operator. Variable labels cannot contain (".").

data

is a data frame or a data matrix (statistical units x manifest variables).

scheme

is a string indicating the type of inner weighting scheme. It is equal to factorial by default. Possible values are centroid or factorial.

tau

indicates the specific quantile that must be considered for the estimation. It is equal to NULL by default, using the quantile default values (0.25, 0.5, 0.75). When specified, tau can be equal to a single value or to a vector, depending on the number of quantiles of interest.

fix.quantile

when equal to TRUE, the quantile used in the iterative procedure of the QC-PM algorithm is fixed to 0.5. It is used when measurement invariance is an issue. It is equal to FALSE by default.

qcorr

is a boolean. If it is equal to TRUE, loadings are estimated by using quantile correlations. By default, it is equal to FALSE.

tol

is a decimal value indicating the tolerance criterion for the iterations (tol=0.00001 by default).

maxiter

is an integer indicating the maximum number of iterations (maxiter=100 by default).

Details

Users can choose to estimate the model parameters for one or more specific quantiles (tau) of interest or to use the default quantile values: tau = (0.25, 0,50, 0.75). If more than one specific quantile is selected, the values must be defined as a numeric vector. It is also possible to fix the quantile to 0.5 in the iterative procedure of the QC-PM algorithm by using the parameter fix.quantile = TRUE for handling the measurement invariance issue (Dolce et al. 2021; Henseler et al. 2016).

Value

An object of class qcpm.

outer.weights

the outer weight estimates for each considered quantile.

outer.loadings

the outer loading estimates for each considered quantile.

path.coefficients

the path coefficient estimates for each considered quantile.

latent.scores

list of the composite scores for each considered quantile.

data

original dataset used for the analysis.

model

internal parameters related to the model estimation.

Author(s)

Cristina Davino, Pasquale Dolce, Giuseppe Lamberti, Domenico Vistocco

References

Davino, C., Dolce, P., Taralli, S. and Vistocco, D. (2020). Composite-based path modeling for conditional quantiles prediction. An application to assess health differences at local level in a well-being perspective. Social Indicators Research, doi:10.1007/s11205-020-02425-5.

Davino, C. and Esposito Vinzi, V. (2016). Quantile composite-based path modeling. Advances in Data Analysis and Classification, 10 (4), pp. 491–520, doi:10.1007/s11634-015-0231-9.

Dolce, P., Davino, C. and Vistocco, D. (2021). Quantile composite-based path modeling: algorithms, properties and applications. Advances in Data Analysis and Classification, doi:10.1007/s11634-021-00469-0.

Henseler J., Ringle, C.M. and Sarstedt, M. (2016). Testing measurement invariance of composites using partial least squares. International Marketing Review, 33 (3), pp. 405–431, doi:10.1108/IMR-09-2014-0304

Li, G., Li, Y. and Tsai, C. (2014). Quantile correlations and quantile autoregressive modeling. Journal of the American Statistical Association, 110 (509) pp. 246–261, doi: 10.1080/01621459.2014.892007

See Also

summary, assessment, boot, and reliability

Examples

# Example of QC-PM in Well-Being analysis
# model with three LVs and reflective indicators

# load library and dataset province
library(qcpm)
data(province)

# Define the model using laavan sintax. Use a set of regression formulas defining 
# firstly the structural model and then the measurement model
model <- "
ECOW ~ EDU
HEALTH ~ EDU + ECOW

# Reflective measurement model
EDU =~ EDU1 + EDU2 + EDU3 + EDU4 + EDU5 + EDU6 + EDU7
ECOW =~ ECOW1 + ECOW2 + ECOW3 + ECOW4 + ECOW5 + ECOW6
HEALTH =~  HEALTH1 + HEALTH2 + HEALTH3
"

# Apply qcpm
well.qcpm = qcpm(model,province)
well.qcpm