{"Package":"investr","Type":"Package","Title":"Inverse Estimation/Calibration Functions","Version":"1.4.0","Author":"Brandon M. Greenwell","Maintainer":"Brandon M. Greenwell ","Description":"Functions to facilitate inverse estimation (e.g., calibration) in\nlinear, generalized linear, nonlinear, and (linear) mixed-effects models. A\ngeneric function is also provided for plotting fitted regression models with\nor without confidence/prediction bands that may be of use to the general\nuser.","Date":"2016-04-08","License":"GPL (>= 2)","URL":"https://github.com/bgreenwell/investr","Depends":"base,","Suggests":"boot, datasets, knitr, MASS, testthat,","Imports":"graphics, nlme, stats, utils,","LazyLoad":"true","LazyData":"true","RoxygenNote":"5.0.1","NeedsCompilation":"no","Packaged":"2016-04-08 23:27:20 UTC; w108bmg","Repository":"CRAN","Date/Publication":"2016-04-09 09:39:09","readme":"# investr: Inverse Estimation in R\n\n[![CRAN\\_Status\\_Badge](http://www.r-pkg.org/badges/version/investr)](http://cran.r-project.org/package=investr)\n[![Build Status](https://travis-ci.org/bgreenwell/investr.svg?branch=master)](https://travis-ci.org/bgreenwell/investr)\n[![Coverage Status](https://img.shields.io/codecov/c/github/bgreenwell/investr.svg)](https://codecov.io/github/bgreenwell/investr?branch=master)\n[![Downloads](http://cranlogs.r-pkg.org/badges/investr)](http://cranlogs.r-pkg.org/badges/investr)\n[![Total Downloads](http://cranlogs.r-pkg.org/badges/grand-total/investr)](http://cranlogs.r-pkg.org/badges/grand-total/investr)\n\nInverse estimation, also referred to as the calibration problem, is a classical and well-known problem in regression. In simple terms, it involves the use of an observed value of the response (or specified value of the mean response) to make inference on the corresponding unknown value of the explanatory variable. \n\nA detailed introduction to investr has been published in The R Journal: \"investr: An R Package for Inverse Estimation\", http://journal.r-project.org/archive/2014-1/greenwell-kabban.pdf. You can track development at https://github.com/bgreenwell/investr. To report bugs or issues, contact the main author directly or submit them to https://github.com/bgreenwell/investr/issues. \n\nAs of right now, `investr` supports (univariate) inverse estimation with objects of class:\n\n* `lm` - linear models (multiple predictor variables allowed)\n* `glm` - generalized linear models (multiple predictor variables allowed)\n* `nls` - nonlinear least-squares models\n* `lme` - linear mixed-effects models (fit using the `nlme` package)\n\n## Installation\n\nThe package is [currently listed on CRAN](http://cran.r-project.org/package=investr) and can easily be installed:\n```r\n # Install from CRAN\n install.packages(\"investr\", dep = TRUE)\n```\nThe package is also part of the [ChemPhys task view](http://cran.r-project.org/web/views/ChemPhys.html), a collection of R packages useful for analyzing data from chemistry and physics experiments. These packages can all be installed at once (including `investr`) using the `ctv` package (Zeileis, 2005):\n```r\n # Install the ChemPhys task view\n install.packages(\"ctv\")\n ctv::install.views(\"ChemPhys\")\n```\n\n## Examples\n\n### Dobson's Beetle Data\n\nIn binomial regression, the estimated lethal dose corresponding to a specific probability _p_ of death is often referred to as _LDp_. `invest` obtains an estimate of _LDp_ by inverting the fitted mean response on the link scale. Similarly, a confidence interval for _LDp_ can be obtained by inverting a confidence interval for the mean response on the link scale.\n```r\nlibrary(investr)\n\n# Dobson's beetle data\nhead(beetle)\n\n# Binomial regression\nbinom_fit <- glm(cbind(y, n-y) ~ ldose, data = beetle, \n family = binomial(link = \"cloglog\"))\nplotFit(binom_fit, lwd.fit = 2, cex = 1.2, pch = 21, bg = \"lightskyblue\", \n lwd = 2, xlab = \"Log dose\", ylab = \"Probability\")\n\n# Inverse estimation\ninvest(binom_fit, y0 = 0.5) # median lethal dose\ninvest(binom_fit, y0 = 0.9) # 90% lethal dose\ninvest(binom_fit, y0 = 0.99) # 99% lethal dose\n\n\n# estimate lower upper \n# 1.7788 1.7702 1.7862\n```\n![Alt text](https://raw.githubusercontent.com/bgreenwell/investr/master/beetle_plotFit.png)\n\nTo obtain an estimate of the standard error, we can use the Wald method:\n```r\ninvest(binom_fit, y0 = 0.5, interval = \"Wald\")\n\n# estimate lower upper se \n# 1.7788 1.7709 1.7866 0.0040\n\n# The MASS package function dose.p works too \nMASS::dose.p(binom_fit, p = 0.5)\n\n# Dose SE\n# p = 0.5: 1.778753 0.00400654\n```\n\n### Including a factor variable\n\nMultiple predictor variables are allowed for objects of class `lm` and `glm`. \nFor instance, the example from `?MASS::dose.p` can be re-created as follows:\n```r\n\n# Load package, assuming it is already installed\nlibrary(MASS)\n\n# Data\nldose <- rep(0:5, 2)\nnumdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)\nsex <- factor(rep(c(\"M\", \"F\"), c(6, 6)))\nSF <- cbind(numdead, numalive = 20 - numdead)\nbudworm <- data.frame(ldose, numdead, sex, SF)\n\n# Logistic regression\nbudworm.lg0 <- glm(SF ~ sex + ldose - 1, family = binomial, data = budworm)\n\n# Using dose.p function from package MASS\ndose.p(budworm.lg0, cf = c(1, 3), p = 1/4)\n\n# Dose SE\n# p = 0.25: 2.231265 0.2499089\n\n# Using invest function from package investr\ninvest(budworm.lg0, y0 = 1/4, \n interval = \"Wald\",\n x0.name = \"ldose\", \n newdata = data.frame(sex = \"F\"))\n \n# estimate lower upper se \n# 2.2313 1.7415 2.7211 0.2499\n```\n\n### Bioassay on Nasturtium\n\nThe data here contain the actual concentrations of an agrochemical present in soil samples versus the weight of the plant after three weeks of growth. These data are stored in the data frame `nasturtium` and are loaded with the package. A simple\nlog-logistic model describes the data well:\n```r\n# Log-logistic model\nlog_fit <- nls(weight ~ theta1/(1 + exp(theta2 + theta3 * log(conc))),\n start = list(theta1 = 1000, theta2 = -1, theta3 = 1),\n data = nasturtium)\nplotFit(log_fit, lwd.fit = 2)\n```\n![Alt text](https://raw.githubusercontent.com/bgreenwell/investr/master/nasturtium_plotFit.png)\n\nThree new replicates of the response (309, 296, 419) at an unknown concentration of interest ($x_0$) are measured. It is desired to estimate $x_0$.\n```r \n# Inversion method\ninvest(log_fit, y0 = c(309, 296, 419), interval = \"inversion\")\n\n# estimate lower upper \n# 2.2639 1.7722 2.9694\n\n# Wald method\ninvest(log_fit, y0 = c(309, 296, 419), interval = \"Wald\") \n\n# estimate lower upper se \n# 2.2639 1.6889 2.8388 0.2847\n```\n\nThe intervals both rely on large sample results and normality. In practice, the bootstrap may be more reliable:\n```r\n# Bootstrap calibration intervals (may take a few seconds)\nboo <- invest(log_fit, y0 = c(309, 296, 419), interval = \"percentile\", \n nsim = 9999, seed = 101, progress = TRUE)\nboo # print bootstrap summary\n\n# estimate lower upper se bias \n# 2.2639 1.7890 2.9380 0.2947 0.0281\n\nplot(boo) # plot results\n```\n![Alt text](https://raw.githubusercontent.com/bgreenwell/investr/master/nasturtium_boot.png)","repoType":"cran"}

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