Maximum Likelihood Estimator: The method of maximum likelihood is the most popular method for deriving estimators - the value of the population parameter T maximizing the likelihood function is used as the estimate of this parameter. The general idea behind maximum likelihood estimation is to find the population that is...

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Statistical Glossary Markov Property: Markov property means "absence of memory" of a random process - that is, independence of conditional probabilities on values U(t2 < t). In simpler words, this property means that future behavior depends only on the current state, but not on the state(s) in the past. See...

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Statistical Glossary Markov Chain: A Markov chain is a series of random values x1, x2, ... in which the probabilities associated with a particular value xi depend only on the prior value . For this reason, a Markov chain is a special case of "memoryless" random processes. The index "i"...

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Linear Model: A linear model specifies a linear relationship between a dependent variable and n independent variables: where y is the dependent variable, {xi} are independent variables, {ai} are parameters of the model. For example, consider that for a sample of 25 cities, the following model was estimated for a...

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Logistic Regression: Logistic regression is used with binary data when you want to model the probability that a specified outcome will occur. Specifically, it is aimed at estimating parameters a and b in the following model: where pi is the probability of a success for given value xi of the...

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Moving Average (MA) Models: Moving average (MA) models are used in time series analysis to describe stationary time series . The MA-models represent time series that are generated by passing the white noise through a non-recursive linear filter . A moving average model of a random process in discrete time...

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Linkage Function: A linkage function is an essential prerequisite for hierarchical cluster analysis . Its value is a measure of the "distance" between two groups of objects (i.e. between two clusters). Algorithms for hierarchical clustering normally differ by the linkage function used. The most common type of linkage functions give...

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Statistical Glossary Linear Filter: A linear filter is the filter whose output is a linear function of the input. Any output value of a linear filter is the weighted mean of input values. In other words, to form one element of the output at time , it is necessary to...

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Likelihood Ratio Test: The likelihood ratio test is aimed at testing a simple null hypothesis against a simple alternative hypothesis. (See Hypothesis for an explanation of "simple hypothesis"). The likelihood ratio test is based on the likelihood ratio r as the test statistic: where X is the observed data (sample),...

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Likelihood Function: Likelihood function is a fundamental concept in statistical inference. It indicates how likely a particular population is to produce an observed sample. Let P(X; T) be the distribution of a random vector X, where T is the vector of parameters of the distribution. If Xo is the observed...

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Latent Variable Growth Curve Models: These techniques, also called Latent Curve Models (LCM), take traditional modeling of growth curves for repeated measures data and extend it to cover the use of latent variables. In Latent Variable Growth Curve Models, Structural Equation Modeling (SEM) methods are used and extended to cover...

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k-Nearest Neighbors Prediction: The k-nearest neighbors (k-NN) prediction is a method to predict a value of a target variable in a given record, using as a reference point a training set of similar objects. The basic idea is to choose k objects from the training set that are closest to...

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k-Nearest Neighbors Classification: The k-nearest neighbors (k-NN) classification is a method of classification that uses a training set chosen from the data as a point of reference in classifying observations. The idea of the method is to find the k elements of the training set that are closest to the...

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k-Means Clustering: The k-means clustering method is used in non-hierarchical cluster analysis . The goal is to divide the whole set of objects into a predefined number (k) of clusters. The criteria for such subdivision is normally the minimal dispersion inside clusters - e.g. the minimal sum of squares of...

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Statistical Glossary Kalman Filter (Equations): The basic mathematics behind the idea of Kalman filter may be described as follows - Consider, for example, a Markov chain - i.e. a random series with Markov property - described by the following equation: (1) where - is the value of the vector-values Markov...

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Statistical Glossary Kalman Filter: Kalman filter is a class of linear filters for predicting and/or smoothing time series. The value of the time series is usually a vector in a state space . Kalman filter is optimal for filtering many types of markov chains . The general structure of this...

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Statistical Glossary Interobserver Reliability: The interobserver reliability of a survey instrument, like a psychological test, measures agreement between two or more subjects rating the same object, phenomenon, or concept. For example, 5 critics are asked to evaluate the quality of 10 different works of art ("objects"), e.g. using scores from...

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Statistical Glossary Intraobserver Reliability: Intraobserver reliability indicates how stable are responses obtained from the same respondent at different time points. The greater the difference between the responses, the smaller the intraobserver reliability of the survey instrument. The correlation coefficient between the responses obtained at different time points from the same...

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Independent Variable: See dependent and independent variables . Browse Other Glossary Entries

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Statistical Glossary Internal Consistency Reliability: The internal consistency reliability of survey instruments (e.g. psychological tests), is a measure of reliability of different survey items intended to measure the same characteristic. For example, there are 5 different questions (items) related to anxiety level. Each question implies a response with 5 possible...

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