# Estimate a Binary Choice Model Use this function to estimate a binary choice model. ```r estim.bin( data, linkFunc = c("logit", "probit"), pcaOptionsX = NULL, costMatrices = NULL, optimOptions = get.options.newton(), aucOptions = get.options.roc(), simFixSize = 0, simTrainFixSize = 0, simTrainRatio = 0.75, simSeed = 0, weightedEval = FALSE, simMaxConditionNumber = Inf ) ``` ## Arguments - `data`: A list that determines data and other required information for the model search process. Use `get.data()` function to generate it from a `matrix` or a `data.frame`. - `linkFunc`: A character string that shows the probability assumption. It can be `logit` or `probit`. - `pcaOptionsX`: A list of options to use principal components of the `x`, instead of the actual values. Set `NULL` to disable. Use `get.options.pca()` for initialization. - `costMatrices`: A list of numeric matrices where each one determines how to score the calculated probabilities. See and use search.bin for more information and initialization. - `optimOptions`: A list for Newton optimization options. Use get.options.newton function to get the options. - `aucOptions`: A list of options for AUC calculation. See and use `[get.options.roc()]` for more information and initialization. - `simFixSize`: An integer that determines the number of out-of-sample simulations. Use zero to disable the simulation. - `simTrainFixSize`: An integer representing the number of data points in the training sample in the out-of-sample simulation. If zero, `trainRatio` will be used. - `simTrainRatio`: A number representing the size of the training sample relative to the available size, in the out-of-sample simulation. It is effective if `trainFixSize` is zero. - `simSeed`: A seed for the random number generator. Use zero for a random value. - `weightedEval`: If `TRUE`, weights will be used in evaluations. - `simMaxConditionNumber`: A number for the maximum value for the condition number in the simulation. ## Details As documented in chapter 12 in if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="greene2010modeling;textual",package="ldt",cached_env=.Rdpack.currefs) , binary regression is a statistical technique used to estimate the probability of one of two possible outcomes for a variable such as $y$, i.e., $p=P(y=1)$ and $q=P(y=0)$. The most commonly used binary regression models are the logit and probit models. In general, a binary regression model can be written as $f(p) = z'\gamma+v$, where the first element in $\gamma$ is the intercept and $f(p)$ is a link function. For logit and probit models we have $f(p) = \ln{\frac{p}{1-p}}$ and $f(p) = \Phi^{-1}(p)$ respectively, where $\Phi^{-1}$ is the inverse cumulative distribution function of the standard normal distribution. Given an independent sample of length $N$, the parameters of the binary regression model are estimated using maximum likelihood estimation. Assuming that some observations are more reliable or informative than others and $w_i$ for $i=1,\ldots,N$ reflects this fact, the likelihood function is given by: $$ L(\gamma) = \prod_{i=1}^N (p_i)^{w_i y_i} (1-p_i)^{w_i (1-y_i)}, $$ where $p_i=\frac{\exp{\gamma z_i}}{1+\exp{\gamma z_i}}$ for logit model and $p_i=\Phi(\gamma z_i)$ for probit model. `ldt` uses feasible GLS to calculate the initial value of the coefficients and a weighted least squares estimator to calculate the initial variance matrix of the error terms (see page 781 in if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="greene2020econometric;textual",package="ldt",cached_env=.Rdpack.currefs) ). The condition number of the estimation is calculated by multiplying 1-norm of the observed information matrix at the maximum likelihood estimator and its inverse (e.g., see page 94 in if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="trefethen1997numerical;textual",package="ldt",cached_env=.Rdpack.currefs) ). Furthermore, if $x$ is a new observations for the explanatory variables, the predicted probability of the positive class is estimated by $p_i=\frac{\exp{\gamma x}}{1+\exp{\gamma x}}$ for logit model and $p_i=\Phi(\gamma x)$ for probit model. Note that the focus in `ldt` is model uncertainty and the main purpose of exporting this method is to show the inner calculations of the search process in search.bin function. ## Examples ```r # Example 1 (simulation, small model): set.seed(123) sample <- sim.bin(3L, 100) print(sample$coef) data <- data.frame(sample$y, sample$x) # Estimate using glm fit <- glm(Y ~ X1 + X2, data = data, family = binomial()) print(fit) # Estimate using 'ldt::estim.bin' fit <- estim.bin(data = get.data(data = data, equations = list(Y ~ X1 + X2)), linkFunc = "logit") print(fit) plot_data <- plot(fit, type = 1) # See 'plot.ldt.estim()' function documentation # Example 2 (simulation, large model with PCA analysis): sample <- sim.bin(30L, 100, probit = TRUE) data <- data.frame(sample$y, sample$x) colnames(data) <- c(colnames(sample$y),colnames(sample$x)) pca_options <- get.options.pca(ignoreFirst = 1, exactCount = 3) fit <- estim.bin(data = get.data(cbind(sample$y, sample$x), endogenous = ncol(sample$y), addIntercept = FALSE), linkFunc = "probit", pcaOptionsX = pca_options) print(fit) plot_data <- plot(fit, type = 2) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also search.bin

estim.bin function