estimate_pattern_long_1d {DySS}

Estimate the Regular Longitudinal Pattern of Univariate Data

Description

Function estimate_pattern_long_1d estimate the regular longitudinal pattern of a univariate variable from a dataset of n subjects. This is usually the first step of dynamic screening. The pattern can be described by mean, variance, covariance, and distribution depending on the estimation method. When the estimated pattern is used for monitoring new subjects, the collected data from new subjects are compared to the estimated pattern for monitoring abnormality.

Usage

estimate_pattern_long_1d(
  data_matrix,
  time_matrix,
  nobs,
  design_interval,
  n_time_units,
  time_unit,
  estimation_method,
  smoothing_method = "local linear",
  bw_mean,
  bw_var,
  bw_cov,
  bw_t,
  bw_y
)

Arguments

data_matrix

observed data arranged in a numeric matrix format.
data_matrix[i,j] is the jth observation of the kth dimension of the ith subject.

time_matrix

observation times arranged in a numeric matrix format.
time_matrix[i,j] is the jth observation time of the ith subject.
data_matrix[i,j] is observed at time_matrix[i,j].

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

estimation_method

a character specifying the estimation method.
If estimation_method="meanvar", the function will estimate the mean and variance functions using local smoothing (c.f., Qiu and Xiang, 2014). Parameters bw_mean and bw_var are required.
If estimation_method="meanvarcov", the function will estimate the mean, variance and covariance functions using local smoothing (c.f., Li and Qiu, 2016). Parameters bw_mean, bw_var and bw_cov are required.
If estimation_method="meanvarcovmean", the function will estimate the mean, variance and covariance functions (c.f., Li and Qiu, 2016). In the last step, the mean function will be updated using the covariance function. Parameters bw_mean, bw_var and bw_cov are required.
If estimation_method="distribution", the function will estimate the distribution function (c.f., You and Qiu, 2020). Parameters bw_t and bw_y are required.
If estimation_method="distributionvarcov", the function will estimate the distribution function and the covariance function of standardized values (c.f., You and Qiu 2020). Parameters bw_cov, bw_t and bw_y are required.

smoothing_method

a character value specifying the smoothing method.
If smoothing_method="local constant", apply local constant approximation.
If smoothing_method="local linear", apply local linear approximation.

bw_mean

a numeric value.
The bandwidth parameter for estimating mean function.

bw_var

a numeric value.
The bandwidth parameter for estimating variance function.

bw_cov

a numeric value.
The bandwidth parameter for estimating covariance function.

bw_t

a numeric value.
The bandwidth parameter in time axis for estimating distribution function.

bw_y

a numeric value.
The bandwidth parameter in y-axis for estimating distribution function.

Details

Estimate the Regular Longitudinal Pattern of Univariate Data

Value

a list that stores the estimated longitudinal pattern and model parameters.
If estimation_method="meanvar", returns a list of class pattern_long_1d_meanvar
If estimation_method="meanvarcov" or "meanvarcovmean", returns a list of class pattern_long_1d_meanvarcov
If estimation_method="distribution", returns a list of class pattern_long_1d_distribution
If estimation_method="distributionvarcov", returns a list of class pattern_long_1d_distributionvarcov

$grid

Discretized design interval.

$mean_est

Estimated mean function.

$var_est

Estimated variance function.

$cov_est

Estimated covariance function.

References

Qiu, P. and Xiang, D. (2014). Univariate dynamic screening system: an approach for identifying individuals with irregular longitudinal behavior. Technometrics, 56:248-260.
Li, J. and Qiu, P. (2016). Nonparametric dynamic screening system for monitoring correlated longitudinal data. IIE Transactions, 48(8):772-786.
You, L. and Qiu, P. (2019). Fast computing for dynamic screening systems when analyzing correlated data. Journal of Statistical Computation and Simulation, 89(3):379-394.
You, L., Qiu, A., Huang, B., and Qiu, P. (2020). Early detection of severe juvenile idiopathic arthritis by sequential monitoring of patients' health-related quality of life scores. Biometrical Journal, 62(5).
You, L. and Qiu, P. (2021). A robust dynamic screening system by estimation of the longitudinal data distribution. Journal of Quality Technology, 53(4).

Examples

data("data_example_long_1d")

result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)