Passing-Bablock regression is a robust regression method for two variables that is symmetric in x and y.

```
pbreg(formula, data, subset, weights, na.action, conf=.95,
nboot = 0, method=1, eps=sqrt(.Machine$double.eps),
x = FALSE, y = FALSE, model = TRUE)
```

pbreg returns an object of `class`

"pbreg".
The generic accessor functions

`coef`

, `fitted`

and `residuals`

extract the relevant components.

- formula
a model formula with a single continuous response on the left and a single continuous predictor on the right.

- data
an optional data frame, list or environment containing the variables in the model.

- subset
an optional vector specifying a subset of observations to be used in the fitting process.

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

I

- na.action
a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of

`options`

. The 'factory fresh' default for R is`na.omit`

, the`na.exclude`

option is often useful.- conf
the width of the computed confidence limit

- nboot
number of bootstrap samples used to compute standard errors and/or confidence limits.

- method
which of 3 related methods to use for the computation

- eps
the tolerance used to detect tied values in x and y

- x,y, model
logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, or the response) is returned.

Terry Therneau

There are 3 related estimators under this heading. Method 1 is the original Passing-Bablock (1983) method, which is equal to a Theil-Sen estimate symmetric about the y=x line. Method 2 is the first extended method of the 1988 paper, designed to be scale invariant. Method 3 is the second extended method from the 1985 paper, the "scissors" estimate which is symmetric about both the x and y axes, and is also scale invariant.

The default confidence interval estimate is based on that derived by Sen, which is in turn based on the relationship to Kendall's tau. A theoretical justification of this approach for methods 2 and 3 is lacking, and we recommend a bootstrap based confidence interval based on 500-1000 replications.

Passing, H. and Bablock, W. (1983). A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I. J. Clin. Chem. Clin. Biochem. 21:709-720.

Passing, H. and Bablock, W. (1984). Comparison of several regression procedures for method comparison studies and determination of sample size. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part II. J. Clin. Chem. Clin. Biochem. 22:431-435.

Bablock, W., Passing, H., Bender, R. and Schneider, B. (1988). A general regression procedure for method transformations. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part III. J. Clin. Chem. Clin. Biochem. 26:783-790.

`deming`

```
afit1 <- pbreg(aes ~ aas, data= arsenate)
afit2 <- pbreg(aas ~ aes, data= arsenate)
rbind(coef(afit1), coef(afit2)) # symmetric results
1/coef(afit1)[2]
```

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