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Multinomial Probit
In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that the dependent variable can fall into. As such, it is an alternative to the multinomial logit model as one method of multiclass classification. It is not to be confused with the ''multivariate'' probit model, which is used to model correlated binary outcomes for more than one independent variable. General specification It is assumed that we have a series of observations ''Y''''i'', for ''i'' = 1...''n'', of the outcomes of multi-way choices from a categorical distribution of size ''m'' (there are ''m'' possible choices). Along with each observation ''Y''''i'' is a set of ''k'' observed values ''x''''1,i'', ..., ''x''''k,i'' of explanatory variables (also known as independent variables, predictor variables, features, etc.). Some examples: *The observed outcomes might be "has disease A, has disease B, has disease C, has none ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Body-mass Index
Body mass index (BMI) is a value derived from the mass (weight) and height of a person. The BMI is defined as the body mass divided by the square of the body height, and is expressed in units of kg/m2, resulting from mass in kilograms (kg) and height in metres (m). The BMI may be determined first by measuring its components by means of a weighing scale and a stadiometer. The multiplication and division may be carried out directly, by hand or using a calculator, or indirectly using a lookup table (or chart). The table displays BMI as a function of mass and height and may show other units of measurement (converted to metric units for the calculation). The table may also show contour lines or colours for different BMI categories. The BMI is a convenient rule of thumb used to broadly categorize a person as based on tissue mass (muscle, fat, and bone) and height. Major adult BMI classifications are ''underweight'' (under 18.5 kg/m2), '' normal weight'' (18.5 to 24.9), ''overweig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probit Model
In 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. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. Conceptual framework Suppose a response variable ''Y'' is ''binary'', that is it can have only two possible o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heteroscedasticity
In statistics, a sequence of random variables is homoscedastic () if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings ''homoskedasticity'' and ''heteroskedasticity'' are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic () results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient. The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance that assume that the modelling errors all have the same variance. While the ordinary least squares ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. Motivation This is sometimes explained with a short story by philosopher Sidney Morgenbesser:Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Variable
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A model with exactly one explanatory variable is a ''simple linear regression''; a model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Variable Model
A latent variable model is a statistical model that relates a set of observable variables (also called ''manifest variables'' or ''indicators'') to a set of latent variables. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. Common use cases for latent variable models include applications in psychometrics (e.g., summarizing responses to a set of survey questions with a factor analysis model positing a smaller number of psychological attributes, such as the trait extraversion, that are presumed to cause the survey question responses), and natural language processing (e.g., a topic model summarizing a corpus of texts with a number of "topics"). It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable ( local independence). Different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the Data generating process, data-generating process. When referring specifically to probability, probabilities, the corresponding term is probabilistic model. All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). Introduction Informally, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blood Pressure
Blood pressure (BP) is the pressure of Circulatory system, circulating blood against the walls of blood vessels. Most of this pressure results from the heart pumping blood through the circulatory system. When used without qualification, the term "blood pressure" refers to the pressure in a brachial artery, where it is most commonly measured. Blood pressure is usually expressed in terms of the systolic pressure (maximum pressure during one Cardiac cycle, heartbeat) over diastolic pressure (minimum pressure between two heartbeats) in the cardiac cycle. It is measured in Millimetre of mercury, millimetres of mercury (mmHg) above the surrounding atmospheric pressure, or in Pascal (unit), kilopascals (kPa). The difference between the systolic and diastolic pressures is known as pulse pressure, while the average pressure during a cardiac cycle is known as mean arterial pressure. Blood pressure is one of the vital signs—together with respiratory rate, heart rate, Oxygen saturation (me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1 p. 1–34Abstract ( 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference." An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships." Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Econome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Variable
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. In pure mathematics In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers)Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183 and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is , and the most common symbol for the output is ; the function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Distribution
In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of ''K'' possible categories, with the probability of each category separately specified. There is no innate underlying ordering of these outcomes, but numerical labels are often attached for convenience in describing the distribution, (e.g. 1 to ''K''). The ''K''-dimensional categorical distribution is the most general distribution over a ''K''-way event; any other discrete distribution over a size-''K'' sample space is a special case. The parameters specifying the probabilities of each possible outcome are constrained only by the fact that each must be in the range 0 to 1, and all must sum to 1. The categorical distribution is the generalization of the Bernoulli distribution for a categorical random variable, i.e. for a dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
