Environmental and geographical factors affecting the Iberian
... (GLMs) (Crawley, 1993), to analyse the relationship between the presence /absence dependent variable and the continuous and dummy explanatory variables (see Guisan et al., 2002; Lehmann et al., 2002). GLMs are an extension of linear models that allow for nonlinearity in the data and also a range of ...
... (GLMs) (Crawley, 1993), to analyse the relationship between the presence /absence dependent variable and the continuous and dummy explanatory variables (see Guisan et al., 2002; Lehmann et al., 2002). GLMs are an extension of linear models that allow for nonlinearity in the data and also a range of ...
Get a pdf file with tutorial slides.
... particular objective may be to learn the conditional expectation E(y x = x), conditional median M(y x = x), or another point predictor of y conditional on an event {x = x}. Suppose that a sampling process draws persons at random from J and realizations of (y, x) may be observable in whole, in part, ...
... particular objective may be to learn the conditional expectation E(y x = x), conditional median M(y x = x), or another point predictor of y conditional on an event {x = x}. Suppose that a sampling process draws persons at random from J and realizations of (y, x) may be observable in whole, in part, ...
Qualitative and Limited Dependent Variable
... individual is equally likely to choose car or bus transportation. The slope of the probit function p = Φ(z) is at its maximum when z = 0, the borderline case. ...
... individual is equally likely to choose car or bus transportation. The slope of the probit function p = Φ(z) is at its maximum when z = 0, the borderline case. ...
The multi-model ensemble (MME) forecast constructed with bias
... the predictor variables used here are precipitation and 850hPa temperature. ...
... the predictor variables used here are precipitation and 850hPa temperature. ...
Finding Optimal Cutpoints for Continuous Covariates
... covariate can be drastically overestimated with this dichotomization approach due to the series of statistical tests. Several alternative methods attempt to correct this problem: (1) significance level (α) adjustment, (2) p-value adjustment, and (3) cross-validation / split sample approach. The simp ...
... covariate can be drastically overestimated with this dichotomization approach due to the series of statistical tests. Several alternative methods attempt to correct this problem: (1) significance level (α) adjustment, (2) p-value adjustment, and (3) cross-validation / split sample approach. The simp ...
Least squares
The method of least squares is a standard approach in regression analysis to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. ""Least squares"" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.The most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model. When the problem has substantial uncertainties in the independent variable (the x variable), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.Least squares problems fall into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. The non-linear problem is usually solved by iterative refinement; at each iteration the system is approximated by a linear one, and thus the core calculation is similar in both cases.Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.When the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator.The following discussion is mostly presented in terms of linear functions but the use of least-squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least-squares method may be used to fit a generalized linear model.For the topic of approximating a function by a sum of others using an objective function based on squared distances, see least squares (function approximation).The least-squares method is usually credited to Carl Friedrich Gauss (1795), but it was first published by Adrien-Marie Legendre.