R/rank_regression.R
rank_regression.Rd
This function fits a regression model to a linearized parametric lifetime distribution for complete and (multiple) rightcensored data. The parameters are determined in the frequently used (log)locationscale parameterization.
For the Weibull, estimates are additionally transformed such that they are in line with the parameterization provided by the stats package (see Weibull).
rank_regression(x, ...) # S3 method for wt_cdf_estimation rank_regression( x, distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic", "weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2"), conf_level = 0.95, direction = c("x_on_y", "y_on_x"), control = list(), options = list(), ... )
x  A 

...  Further arguments passed to or from other methods. Currently not used. 
distribution  Supposed distribution of the random variable. 
conf_level  Confidence level of the interval. 
direction  Direction of the dependence in the regression model. 
control  A list of control parameters (see optim).

options  A list of named options. See 'Options'. 
A list with classes wt_model
, wt_rank_regression
and wt_model_estimation
which contains:
coefficients
: A named vector of estimated coefficients (parameters of the
assumed distribution). Note: The parameters are given in the
(log)locationscaleparameterization.
confint
: Confidence intervals for the (log)locationscale parameters.
For threshold distributions no confidence interval for the threshold parameter
can be computed. If direction = "y_on_x"
, backtransformed confidence
intervals are provided.
shape_scale_coefficients
: Only included if distribution
is "weibull"
or "weibull3"
(parameterization used in Weibull).
shape_scale_confint
: Only included if distribution
is "weibull"
or "weibull3"
. Approximated confidence intervals for scale \(\eta\) and
shape \(\beta\) (and threshold \(\gamma\) if distribution = "weibull3"
).
varcov
: Only provided if options = list(conf_method = "HC")
(default).
Estimated heteroscedasticityconsistent (HC) variancecovariance matrix
for the (log)locationscale parameters.
r_squared
: Coefficient of determination.
data
: A tibble
with class wt_cdf_estimation
returned by estimate_cdf.
distribution
: Specified distribution.
direction
: Specified direction.
If more than one method was specified in estimate_cdf, the resulting output
is a list with class wt_model_estimation_list
. In this case, each list element
has classes wt_rank_regression
and wt_model_estimation
, and the items listed
above, are included.
The confidence intervals of the parameters are computed on the basis of a heteroscedasticityconsistent (HC) covariance matrix. Here it should be said that there is no statistical foundation to determine the standard errors of the parameters using Least Squares in context of Rank Regression. For an accepted statistical method use maximum likelihood.
If options = list(conf_method = "Mock")
, the argument distribution
must be
one of "weibull"
and "weibull3"
. The approximated confidence intervals
for the Weibull parameters can then only be estimated on the following
confidence levels (see 'References' (Mock, 1995)):
conf_level = 0.90
conf_level = 0.95
conf_level = 0.99
Argument options
is a named list of options:
Name  Value 
conf_method  "HC" (default) or "Mock" 
Mock, R., Methoden zur Datenhandhabung in Zuverlässigkeitsanalysen, vdf Hochschulverlag AG an der ETH Zürich, 1995
Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998
# Reliability data preparation: ## Data for twoparametric model: data_2p < reliability_data( shock, x = distance, status = status ) ## Data for threeparametric model: data_3p < reliability_data( alloy, x = cycles, status = status ) # Probability estimation: prob_tbl_2p < estimate_cdf( data_2p, methods = "johnson" ) prob_tbl_3p < estimate_cdf( data_3p, methods = "johnson" ) prob_tbl_mult < estimate_cdf( data_3p, methods = c("johnson", "kaplan") ) # Example 1  Fitting a twoparametric weibull distribution: rr_2p < rank_regression( x = prob_tbl_2p, distribution = "weibull" ) # Example 2  Fitting a threeparametric lognormal distribution: rr_3p < rank_regression( x = prob_tbl_3p, distribution = "lognormal3", conf_level = 0.99 ) # Example 3  Fitting a threeparametric lognormal distribution using # direction and control arguments: rr_3p_control < rank_regression( x = prob_tbl_3p, distribution = "lognormal3", conf_level = 0.99, direction = "y_on_x", control = list(trace = TRUE, REPORT = 1) )#> iter 1 value 0.976393 #> iter 2 value 0.989504 #> iter 3 value 0.991362 #> iter 4 value 0.991368 #> iter 5 value 0.991383 #> iter 6 value 0.991383 #> iter 7 value 0.991383 #> final value 0.991383 #> converged# Example 4  Fitting a threeparametric loglogistic distribution if multiple # methods in estimate_cdf were specified: rr_lists < rank_regression( x = prob_tbl_mult, distribution = "loglogistic3", conf_level = 0.90 )