Probit modelIn statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model.
Ordered logitIn statistics, the ordered logit model (also ordered logistic regression or proportional odds model) is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. For example, if one question on a survey is to be answered by a choice among "poor", "fair", "good", "very good" and "excellent", and the purpose of the analysis is to see how well that response can be predicted by the responses to other questions, some of which may be quantitative, then ordered logistic regression may be used.
Generalized linear modelIn statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.
Controlled-access highwayA controlled-access highway is a type of highway that has been designed for high-speed vehicular traffic, with all traffic flow—ingress and egress—regulated. Common English terms are freeway, motorway and expressway. Other similar terms include throughway (or thruway) and parkway. Some of these may be limited-access highways, although this term can also refer to a class of highways with somewhat less isolation from other traffic. In countries following the Vienna convention, the motorway qualification implies that walking and parking are forbidden.
Ramp meterA ramp meter, ramp signal, or metering light is a device, usually a basic traffic light or a two-section signal light (red and green only, no yellow) together with a signal controller, that regulates the flow of traffic entering freeways according to current traffic conditions. Ramp meters are used at freeway on-ramps to manage the rate of automobiles entering the freeway. Ramp metering systems have proved to be successful in decreasing traffic congestion and improving driver safety.
Ontario Highway 401King's Highway 401, commonly referred to as Highway 401 and also known by its official name as the Macdonald–Cartier Freeway or colloquially referred to as the four-oh-one, is a controlled-access 400-series highway in the Canadian province of Ontario. It stretches from Windsor in the west to the Ontario–Quebec border in the east. The part of Highway 401 that passes through Toronto is North America's busiest highway, and one of the widest.
Discrete choiceIn economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis.
Ordinal regressionIn statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. It can be considered an intermediate problem between regression and classification. Examples of ordinal regression are ordered logit and ordered probit.
Traffic flowIn mathematics and transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems.
Logistic regressionIn statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).
LogitIn statistics, the logit (ˈloʊdʒɪt ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function , so the logit is defined as Because of this, the logit is also called the log-odds since it is equal to the logarithm of the odds where p is a probability. Thus, the logit is a type of function that maps probability values from to real numbers in , akin to the probit function.
Ordinal dataOrdinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute.
Segmented regressionSegmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.
Toll roadA toll road, also known as a turnpike or tollway, is a public or private road (almost always a controlled-access highway in the present day) for which a fee (or toll) is assessed for passage. It is a form of road pricing typically implemented to help recoup the costs of road construction and maintenance. Toll roads have existed in some form since antiquity, with tolls levied on passing travelers on foot, wagon, or horseback; a practice that continued with the automobile, and many modern tollways charge fees for motor vehicles exclusively.
Dual carriagewayA dual carriageway (BrE) or a divided highway (AmE) is a class of highway with carriageways for traffic travelling in opposite directions separated by a central reservation (BrE) or median (AmE). Roads with two or more carriageways which are designed to higher standards with controlled access are generally classed as motorways, freeways, etc., rather than dual carriageways. A road without a central reservation is known as a single carriageway regardless of how many lanes there are.
Piecewise linear functionIn mathematics and statistics, a piecewise linear, PL or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".
PiecewiseIn mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself. A distinct, but related notion is that of a property holding piecewise for a function, used when the domain can be divided into intervals on which the property holds.
High-occupancy vehicle laneA high-occupancy vehicle lane (also known as an HOV lane, carpool lane, diamond lane, 2+ lane, and transit lane or T2 or T3 lanes) is a restricted traffic lane reserved for the exclusive use of vehicles with a driver and two or more passengers, including carpools, vanpools, and transit buses. These restrictions may be only imposed during peak travel times or may apply at all times. There are different types of lanes: temporary or permanent lanes with concrete barriers, two-directional or reversible lanes, and exclusive, concurrent, or contraflow lanes working in peak periods.
Multivariate adaptive regression splineIn statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables. The term "MARS" is trademarked and licensed to Salford Systems. In order to avoid trademark infringements, many open-source implementations of MARS are called "Earth". This section introduces MARS using a few examples.
