The mblm Package. August 12, License GPL version 2 or newer. confint.mblm. mblm... 3 summary.mblm...
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1 The mblm Package August 12, 2005 Type Package Title Median-Based Linear Models Version 0.1 Date Author Lukasz Komsta Maintainer Lukasz Komsta Description This package provides linear models based on Theil-Sen single median and Siegel repeated medians. They are very robust (29 or 50 percent breakdown point, respectively), and if no outliers are present, the estimators are very similar to OLS. License GPL version 2 or newer. URL R topics documented: confint.mblm mblm summary.mblm Index 6 confint.mblm Confidence Intervals for mblm Model Description Computes confidence intervals for one or more parameters in a fitted model of mblm class. Usage confint.mblm(object, parm, level = 0.95,...) 1
2 2 confint.mblm Arguments object parm level a fitted model object a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. Not yet implemented for mblm the confidence level required... additional arguments Details This function computes confidence intervals for slope and intercept in linear model based on single median or repeated medians. The confidence intervals are computed in simpliest way, as confidence interval for the median of all slopes or intercepts found during fitting. Value A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. Note The recommended method of calculating confidence intervals, given by Sen and based on Kendall s tau, not Wilcoxon test, is not implemented at this time and is considered to be implemented in next version of this package. Author(s) Lukasz Komsta References Sen, P.K. (1968). Estimates of Regression Coefficient Based on Kendall s tau. J. Am. Stat. Ass. 63, 324, See Also mblm, summary.mblm Examples set.seed(1234) x <- 1:100+rnorm(100) y <- x+rnorm(100) y[100] <- 200 fit <- mblm(y~x) fit summary(fit) confint(fit)
3 mblm 3 mblm Fitting Median-Based Linear Models Description Usage This function is used to fit linear models based on Theil-Sen single median, or Siegel repeated medians. mblm(formula, dataframe, repeated = TRUE) Arguments formula dataframe repeated A formula of type y ~ x (only linear models are accepted) Optional dataframe If set to true, model is computed using repeated medians. If false, a single median estimators are calculated Details Value Theil-Sen single median method computes slopes of lines crossing all possible pairs of points, when x coordinates differ. After calculating these n(n-1)/2 slopes (these value are true only if x is distinct), the median of them is taken as slope estimator. Next, the intercepts of n lines, crossing each point and having calculated slope are calculated. The median from them is intercept estimator. Siegel repeated medians is more complicated. For each point, the slopes between it and the others are calcuated (resulting n-1 slopes) and the median is taken. This results in n medians and median from this medians is slope estimator. Intercept is calculated in similar way, for more information please take a look in function source. The breakdown point of Theil-Sen method is about 29%, Siegel extended it to 50%, so these regression methods are very robust. Additionally, if the errors are normally distributed and no outliers are present, the estimators are very similar to classic least squares. An object of class c("mblm","lm"), containing minimal set of data to perform basic operations, such as in case of lm model. Additionally, the return value contains 2 fields: slopes intercepts The slopes (in single median), or medians of slopes (in repeated medians) between tested point pairs The intercepts calculated Note This function should have compatibility with all lm methods, but it is not guaranteed that they will work or have any cognitive value (this method is nonparametric). The compatibility was only introduced to use some basic methods from lm without programming new functions. Author(s) Lukasz Komsta
4 4 summary.mblm References Theil, H. (1950) A rank invariant method for linear and polynomial regression analysis. Nederl. Akad. Wetensch. Proc. Ser. A 53, (Part I), (Part II), (Part III). Sen, P.K. (1968). Estimates of Regression Coefficient Based on Kendall s tau. J. Am. Stat. Ass. 63, 324, See Also Siegel, A.F. (1982). Robust Regression Using Repeated Medians. Biometrika, 69, 1, lm, summary.mblm, confint.mblm Examples set.seed(1234) x <- 1:100+rnorm(100) y <- x+rnorm(100) y[100] <- 200 fit <- mblm(y~x) fit summary(fit) fit2 <- lm(y~x) plot(x,y) abline(fit) abline(fit2,lty=2) plot(fit) residuals(fit) fitted(fit) plot(density(fit$slopes)) plot(density(fit$intercepts)) anova(fit) anova(fit2) anova(fit,fit2) confint(fit) AIC(fit,fit2) summary.mblm Summarizing median-based linear models Description summary method for class mblm Usage summary.mblm(object,...) Arguments object an object of class mblm, usually, a result of a call to mblm.... additional arguments
5 summary.mblm 5 Details Value Note This function is based on summary.lm code, and the base difference is use of nonparametric wilcox.test to obtain significance and mad instead of standard error of estimates. Of course you can force standard lm behavior by calling summary.lm, but values received in such way has low cognitive value. For the return value, see summary.lm. Summary of mblm class does not contain R-squared values and F-test result. The significance of estimators can be computed more "lege artis" based on Kendall s tau, as suggested by Sen, but today such feature is not yet implemented. Author(s) Lukasz Komsta References Theil, H. (1950) A rank invariant method for linear and polynomial regression analysis. Nederl. Akad. Wetensch. Proc. Ser. A 53, (Part I), (Part II), (Part III). Sen, P.K. (1968). Estimates of Regression Coefficient Based on Kendall s tau. J. Am. Stat. Ass. 63, 324, See Also Siegel, A.F. (1982). Robust Regression Using Repeated Medians. Biometrika, 69, 1, summary.lm, mblm, confint.mblm Examples set.seed(1234) x <- 1:10+rnorm(10) y <- x+rnorm(10) y[10] <- 20 fit <- mblm(y~x) summary(fit)
6 Index Topic models confint.mblm, 1 mblm, 2 summary.mblm, 4 confint.mblm, 1, 3, 5 lm, 3 mblm, 2, 2, 5 summary.lm, 4, 5 summary.mblm, 2, 3, 4 6
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Type Package Package GWRM July 31, 2017 Title Generalized Waring Regression Model for Count Data Version 2.1.0.3 Date 2017-07-18 Maintainer Antonio Jose Saez-Castillo Depends R (>= 3.0.0)
Fathom Dynamic Data TM Version 2 Specifications
Data Sources Fathom Dynamic Data TM Version 2 Specifications Use data from one of the many sample documents that come with Fathom. Enter your own data by typing into a case table. Paste data from other