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Deming Regression

Source: R/dem_reg.R
dem_reg.Rd

[Stable]

A function for fitting a straight line to two-dimensional data (i.e., X and Y) that are measured with error.

Usage

dem_reg(
  x,
  y,
  id = NULL,
  data,
  conf.level = 0.95,
  weighted = FALSE,
  weights = NULL,
  error.ratio = 1,
  keep_data = FALSE,
  compute_joint = TRUE
)

Arguments

x

Name of column with first measurement.

y

Name of other column with the other measurement to compare to the first.

id

Column with subject identifier.

data

Data frame with all data.

conf.level

The confidence level required. Default is 95%.

weighted

Logical indicator (TRUE/FALSE) for whether to use weighted Deming regression. Default is FALSE.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector.

error.ratio

Ratio of the two error variances. Default is 1. This argument is ignored if subject identifiers are provided.

keep_data

Logical indicator (TRUE/FALSE). If TRUE, the jacknife samples are returned; default is FALSE. Users may wish to set to FALSE if data is especially large.

compute_joint

Logical indicator (TRUE/FALSE). If TRUE, joint confidence region is computed. Default is TRUE.

Value

The function returns a simple_eiv (eiv meaning "error in variables") object.

  • call: The matched call.

  • model: Data frame presenting the results from the Deming regression analysis.

  • resamples: List containing resamples from jacknife procedure.

  • vcov: Variance-covariance matrix for slope and intercept.

  • joint_region: Joint confidence region ellipse coordinates (if compute_joint = TRUE).

  • joint_test: Test of whether ideal point is enclosed by joint region.

Details

This function provides a Deming regression analysis wherein the sum of distances in both x and y direction is minimized. Deming regression, also known as error-in-variable regression, is useful in situations where both X & Y are measured with error. The use of Deming regression is beneficial when comparing to methods for measuring the same continuous variable.

Currently, the dem_reg function covers simple Deming regression and weighted Deming regression. Weighted Deming regression can be used by setting the weighted argument to TRUE. The weights can be provided by the user or can be calculated within function.

If the data are measured in replicates, then the measurement error can be directly derived from the data. This can be accomplished by indicating the subject identifier with the id argument. When the replicates are not available in the data, then the ratio of error variances (y/x) can be provided with the error.ratio argument.

When compute_joint = TRUE, the function computes the joint (slope, intercept) confidence region based on the chi-square distribution with 2 degrees of freedom. This elliptical region accounts for the correlation between slope and intercept estimates and can provide improved power for detecting deviations from (null) hypothesized values (e.g., slope = 1, intercept = 0).

References

Linnet, K. (1990) Estimation of the linear relationship between the measurements of two methods with proportional errors. Statistics in Medicine, 9, 1463-1473.

Linnet, K. (1993). Evaluation of regression procedures for methods comparison studies. Clinical chemistry, 39, 424-432.

Sadler, W.A. (2010). Joint parameter confidence regions improve the power of parametric regression in method-comparison studies. Accreditation and Quality Assurance, 15, 547-554.