On the Interpolation of Data with Normally Distributed Uncertainty for
... This can obviously lead to poor decision making. Therefore, it is vital to integrate our knowledge about the uncertainty of the data into our visualizations. As we will see, this not only helps to raise awareness for the existence and magnitude of the uncertainty, but will also allow us to make bett ...
... This can obviously lead to poor decision making. Therefore, it is vital to integrate our knowledge about the uncertainty of the data into our visualizations. As we will see, this not only helps to raise awareness for the existence and magnitude of the uncertainty, but will also allow us to make bett ...
Modeling Economic Output and Economic Growth with
... The original neoclassical growth model from economists Solow (1956) and Swan (1956) suggest that the GDP of poor countries will - under the right conditions - grow faster than the GDP of rich countries, which is why the starting level of income must be of importance to economic growth. The models di ...
... The original neoclassical growth model from economists Solow (1956) and Swan (1956) suggest that the GDP of poor countries will - under the right conditions - grow faster than the GDP of rich countries, which is why the starting level of income must be of importance to economic growth. The models di ...
Document
... Deviance residuals plot The plot of deviance residuals against either time, observation number or acceleration factor should look like random noise. Otherwise, it is an indication of some inadequacy of the model. resi=residuals(larynx.weibull, type="deviance") ...
... Deviance residuals plot The plot of deviance residuals against either time, observation number or acceleration factor should look like random noise. Otherwise, it is an indication of some inadequacy of the model. resi=residuals(larynx.weibull, type="deviance") ...
Document
... independent variable x. Use the sample data to estimate unknown parameters in the model. Specify the probability distribution of the random error term and estimate the standard deviation of this distribution. Statistically evaluate the usefulness of the model. When satisfied that the model is useful ...
... independent variable x. Use the sample data to estimate unknown parameters in the model. Specify the probability distribution of the random error term and estimate the standard deviation of this distribution. Statistically evaluate the usefulness of the model. When satisfied that the model is useful ...
Persistence of topographic controls on the spatial distribution of
... component of the random function, (x), describes the residual differences between the model predictions and the actual values. These residuals will likely be spatially correlated, and this spatial correlation can be modeled to improve the predictive ability of the random function. Two distinct type ...
... component of the random function, (x), describes the residual differences between the model predictions and the actual values. These residuals will likely be spatially correlated, and this spatial correlation can be modeled to improve the predictive ability of the random function. Two distinct type ...
Phylogenetic Logistic Regression for Binary Dependent Variables
... outcome of fitting the model to data may be an indication that the residuals contain no phylogenetic signal, so that the trait in question can be viewed as having evolved along a star phylogeny. In such cases, however, it is important to realize that statistical tests will not be the same as for con ...
... outcome of fitting the model to data may be an indication that the residuals contain no phylogenetic signal, so that the trait in question can be viewed as having evolved along a star phylogeny. In such cases, however, it is important to realize that statistical tests will not be the same as for con ...
Sensitivity analysis for randomised trials with missing outcome data
... If the main analysis assumed MAR (∆ = 0), we propose 1. sensitivity analysis assuming ∆i = δ for all individuals 2. sensitivity analysis assuming ∆i = δ for all in intervention arm; ∆i = 0 for all in control arm 3. sensitivity analysis assuming ∆i = δ for all in control arm; ∆i = 0 for all in interv ...
... If the main analysis assumed MAR (∆ = 0), we propose 1. sensitivity analysis assuming ∆i = δ for all individuals 2. sensitivity analysis assuming ∆i = δ for all in intervention arm; ∆i = 0 for all in control arm 3. sensitivity analysis assuming ∆i = δ for all in control arm; ∆i = 0 for all in interv ...
Sample Size Planning - Chinese University of Hong Kong
... relevant studies, is to use the data from a pilot study to estimate the sample size. In general doing a pilot study is a good idea for many reasons but caution needs to be exercised when using the effect size observed in the pilot study as the estimated effect size for the main study. The main reaso ...
... relevant studies, is to use the data from a pilot study to estimate the sample size. In general doing a pilot study is a good idea for many reasons but caution needs to be exercised when using the effect size observed in the pilot study as the estimated effect size for the main study. The main reaso ...
A survey of econometric methods for mixed
... "ragged-edge" problem, namely, publication delays cause missing values for some of the variables at the end of the sample, see Wallis (1986). As an example, one of the key indicators of macroeconomic activity, the Gross Domestic Product (GDP), is released quarterly and with a considerable publicatio ...
... "ragged-edge" problem, namely, publication delays cause missing values for some of the variables at the end of the sample, see Wallis (1986). As an example, one of the key indicators of macroeconomic activity, the Gross Domestic Product (GDP), is released quarterly and with a considerable publicatio ...
Missing Data in Educational Research: A Review of Reporting
... missing values with the predicted scores from a linear regression equation. Regression imputation is relatively straightforward if missing values are isolated on a single variable (i.e., there is a single, univariate missing-data pattern). In this case the incomplete variable is regressed on other m ...
... missing values with the predicted scores from a linear regression equation. Regression imputation is relatively straightforward if missing values are isolated on a single variable (i.e., there is a single, univariate missing-data pattern). In this case the incomplete variable is regressed on other m ...
Impartial Predictive Modeling: Ensuring Fairness
... covariates w. These are connected through an unknown, joint probability distribution P(Y, x, s, w). Our data consists of n iid draws from this joint distribution. The standard statistical goal is to estimate the conditional expectation of Y given the covariates: Y = E[Y |x, s, w] + u where u has mea ...
... covariates w. These are connected through an unknown, joint probability distribution P(Y, x, s, w). Our data consists of n iid draws from this joint distribution. The standard statistical goal is to estimate the conditional expectation of Y given the covariates: Y = E[Y |x, s, w] + u where u has mea ...
Bivariate censored regression relying on a new estimator of the joint
... where δ{a,b} denotes the Dirac mass at point (a, b). This means that we only put mass at the observations where the two components of Y are uncensored, while the weight Wj is here to take account for bivariate censoring. Dening the weight function Wj depends on the identiability conditions we put ...
... where δ{a,b} denotes the Dirac mass at point (a, b). This means that we only put mass at the observations where the two components of Y are uncensored, while the weight Wj is here to take account for bivariate censoring. Dening the weight function Wj depends on the identiability conditions we put ...
Specification and Diagnostic Tests
... hypothesis under test. Output from a test command consists of the sample values of one or more test statistics and their associated probability numbers (p-values). The latter indicate the probability of obtaining a test statistic whose absolute value is greater than or equal to that of the sample st ...
... hypothesis under test. Output from a test command consists of the sample values of one or more test statistics and their associated probability numbers (p-values). The latter indicate the probability of obtaining a test statistic whose absolute value is greater than or equal to that of the sample st ...
PDF file for Measuring Employment From Birth And Deaths In The Current Employment Statistics Surveye
... industries combined). A system of equations that has a property of this type is referred to as a system of seemingly unrelated regression (SUR) equations. Generalized least squares (GLS) parameter estimates for a system of SUR equations can be derived that take into account the mutually correlated r ...
... industries combined). A system of equations that has a property of this type is referred to as a system of seemingly unrelated regression (SUR) equations. Generalized least squares (GLS) parameter estimates for a system of SUR equations can be derived that take into account the mutually correlated r ...
Appendix S1 Example script to run replications of the quantile count
... Example script to run replications of the quantile count model in R #Script to perform m replications of dithering of count data on multiple taus #based on Machado and Santos Silva (2005 JASA) #Results stored in matrix count.model3.rep50t98 #Confidence intervals can be turned off with rq(ci=F) and t ...
... Example script to run replications of the quantile count model in R #Script to perform m replications of dithering of count data on multiple taus #based on Machado and Santos Silva (2005 JASA) #Results stored in matrix count.model3.rep50t98 #Confidence intervals can be turned off with rq(ci=F) and t ...
spatial chow-lin methods: bayesian and ml forecast comparisons
... Pavia-Miralles and Cabrer-Borras (2007)). Usually constraints are imposed to restrict the predicted unobserved series to add up to the observed lower frequency series, e.g. by specifying penalty functions (see Denton (1971)). The discrepancy between the sum of the predicted high frequency observatio ...
... Pavia-Miralles and Cabrer-Borras (2007)). Usually constraints are imposed to restrict the predicted unobserved series to add up to the observed lower frequency series, e.g. by specifying penalty functions (see Denton (1971)). The discrepancy between the sum of the predicted high frequency observatio ...
Confidence sets for model selection by F
... of scientic understanding of the nature of the data. The second aspect is that it does not give any indication of how reliable the selected model is (in fact, uncertainty measures such as standard errors and condence intervals based on the nal model can be highly misleading). The third issue is t ...
... of scientic understanding of the nature of the data. The second aspect is that it does not give any indication of how reliable the selected model is (in fact, uncertainty measures such as standard errors and condence intervals based on the nal model can be highly misleading). The third issue is t ...
Linear regression
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y. Given a variable y and a number of variables X1, ..., Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ""lack of fit"" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ""least squares"" and ""linear model"" are closely linked, they are not synonymous.