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

Arguments

formula

A formula of the form y ~ x specifying the model. If provided, takes precedence over x and y arguments.

data

Data frame with all data.

id

Column with subject identifier (optional).

x

Name of column with first measurement (deprecated in favor of formula interface).

y

Name of other column with the other measurement to compare to the first (deprecated in favor of formula interface).

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.

model

Logical. If TRUE (default), the model frame is stored in the returned object. This is needed for methods like plot(), fitted(), residuals(), and predict() to work without supplying data. If FALSE, the model frame is not stored (saves memory for large datasets), but these methods will require a data argument.

keep_data

Logical indicator (TRUE/FALSE). If TRUE, the jacknife samples are returned; default is FALSE.

...

Additional arguments (currently unused).

Value

The function returns a simple_eiv (eiv meaning "error in variables") object with the following components:

  • coefficients: Named vector of coefficients (intercept and slope).

  • residuals: Optimized residuals from the fitted model.

  • fitted.values: Estimated true Y values (Y-hat).

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

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

  • df.residual: Residual degrees of freedom.

  • call: The matched call.

  • terms: The terms object used.

  • xlevels: (Only for models with factors) levels of factors.

  • model: The model frame.

  • x_vals: Original x values used in fitting.

  • y_vals: Original y values used in fitting.

  • x_hat: Estimated true X values.

  • y_hat: Estimated true Y values.

  • error.ratio: Error ratio used in fitting.

  • weighted: Whether weighted regression was used.

  • weights: Weights used in fitting.

  • conf.level: Confidence level used.

  • resamples: List containing resamples from jacknife procedure (if keep_data = TRUE).

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.

Interface Change

The x and y arguments are deprecated. Please use the formula interface instead:

  • Old: dem_reg(x = "x_var", y = "y_var", data = df)

  • New: dem_reg(y_var ~ x_var, data = df)

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.

Examples

if (FALSE) { # \dontrun{
# New formula interface (recommended)
model <- dem_reg(y ~ x, data = mydata)

# Old interface (still works with deprecation warning)
model <- dem_reg(x = "x", y = "y", data = mydata)
} # }