Flashcards
Stats Chap 8
Cards in this deck (49)
- 1Adjusted Predicted ValueA measure of the influence of a particular case of data. It is the predicted value of a vase from a model estimated without the case included in the data. The value is calculated by re-estimating the model without the case in question, then using this new model to predict the value of the excluded case. If a case does not exert a large influence over the model then its predicted value should be similar regardless of whether the model is estimated including or excluding that case. The differences between the predicted value of a case from the model when that case was included and the predicted value from the model when it was excluded is the DFFit.
- 2Adjusted R SquaredA measure of the loss of predictive power or shrinkage in regression. Tells us how much variance in the outcome could be accounted for if the model had been derived from the population from which the sample was taken.
- 3AutocorrelationWhen the residuals of two observations in a regression model are correlated.
- 4b(i)Unstandardized regression coefficient. Indicates the strength of relationship between a given predictor, i, of many and an outcome in the units of measurement of the predictor. It is the change in the outcome associated with a unit change in the predictor.
- 5β(i)Standardized regression coefficient. Indicates the strength of relationship between a given predictor, i, of many and an outcome in a standardized form. It is the change in the outcome (in standard deviations) associated with a one standard deviation change in the predictor.
- 6Cook's DistanceA measure of the overall influence of a case on a model. Suggested that values greater than 1 may be cause for concern.
- 7Covariance Ratio (CVR)A measure of whether a case influences the variance of the parameters in a regression model. When this ratio is close to 1 the case has very little influence on the variances of the model parameters. If the CVR of a case is greater than 1+[3(k+1)/n] then deleting that case will damage the precision of some of the model's parameters, but if it is less than 1-[3(k+1)/n] then deleting the case will improve the precision of some of the model's parameters (k is the number of predictors and n is the sample size).
- 8Cross-ValidationAssessing the accuracy of a model across different samples. This is an important step in generalization. In a regression model there are two main methods of cross-validation: adjusted R squared or data splitting, in which the data are split randomly into two halves, and a regression model is estimated from each half and the compared.
- 9Deleted ResidualA measure of the influence of a particular case of data. Is it the difference between the adjusted predicted value for a case and the original observed values for that case.
- 10DFBetaA measure of the influence of a case on the values of bi in a regression model. If we estimated a regression parameter, bi then the difference between these two estimates would be the DFBeta for the case that was deleted. By looking at the values of the DFBetas, it is possible to identify cases that have a large influence on the parameters of the regression model: however, the size of DFBeta will depend on the units of measurement of the regression parameter.
- 11DFFitA measure of the influence of a case. It is the predicted value and the original predicted value of a particular case. If a case is not influential then its DFFit should be zero-- hence, we expect non-influential cases to have small DFFit values. However, we have the problem that this statistic depends on the units of measurement of the outcome and so a DFFit of 0.5 will be very small if the outcome ranges from 1 to 100, but very large if the outcome varies from 0 to 1.
- 12Dummy VariablesA way of recording a categorical variable with more than two categories into a seres of variables all of which are dichotomous and can take on values of only 0 to 1. There are seven basic steps to create such variables: (1) count the number of groups you want to recode and subtract: (2) create as many new variables as the value you calculated in step 1 (these are you dummy variables): (3) choose one of your groups as a baseline (i.e., a group against which all other groups should be compared, such as control group); (4) asking that baseline group values of 0 for all of your dummy variables; (5) for you first dummy variable, assign the value 1 to the first group that you want to compare against the baseline group (assign all other groups 0 for this variable); (6) for the second dummy variable assign the value 1 to the second group that you want to compare against the baseline group (assign all other groups 0 for this variable); (7) repeat this process until you run out of dummy variables.
- 13Durbin-Watson TestA test for serial correlations between errors in regression models. Specifically, it tests whether adjacent residuals are correlated, which is useful in assessing the assumption of independent errors. The test statistic can vary between 0 and 4, with a value of 2 meaning that the residuals are uncorrelated. A value greater than 2 indicates a negative correlation between adjacent residuals, whereas a value below 2 indicates a positive correlation. The size of the Durbin-Watson statistic depends upon the number of predictors in the model and the number of predictors in the model and the number of observations. As a rule of thumb, values less than 1 or greater than 3 are definitely cause for concern; however, values closer to 2 may still be problematic depending on the sample and model.
- 14F-ratioA test statistic with a known probability distribution (the F-distribution). It is the rain of the average validity unexplained by the same model. It is used to test the overall fir of the model in regression and multiple regression, and to test for overall differences between group means in experiments.
- 15GeneralizationThe ability of a statistical model to say something beyond the set of observations that spawned it. If a model generalizes it is assumed that predictions from that model can be applied not just to the sample on which it is based, but to a wider population from which the sample came.
- 16Goodness of FitAn index of how well a model fits the data from which it was generated. It's usually based on how well the data predicted by the model correspond to the data that were actually collected.
- 17Hat ValuesAnother name for leverage.
- 18HeteroscedasticityThe opposite of homoscedasticity. This occurs when the residuals at each level of the predictor variable(s) have unequal variances. Put another way, at each point along any predictor variable, the spread of residuals is different.
- 19Hierarchical RegressionA method of multiple regression in which the order in which predictors are entered into the regression model is determined by the researcher based on previous research variables: variables already known to be predictors are entered first, new variables are entered subsequently.
- 20HomoscedasticityAn assumption in regression analysis that the residuals at each level of the predictor variable(s) have similar variances. Put another way, at each point along any predictor variable, the spread of residuals should be fairly constant.
- 21Independent ErrorsFor any two observations in regression the residuals should be uncorrelated (or independent).
- 22LeverageGauge the influence of the observed value of the outcome variable over the predicted values. The average leverage values is (k+1)/n in which k is the number of predictors in the model and n is the number of participants. Leverage values can lie between 0 (the case has no influence) and 1 (the case has complete influence over prediction). If no cases exert undue influence over the model then we would expect all of the leverage values to be close to the average value.
- 23Mahalanobis DistanceThese measure the influence of a case by examining the distance of vases from the mean(s) of the predictor variable(s). One needs to look at the cases with the highest values. It is not east to establish a cut-off point at which to worry. Even with large samples (N=500) and five predictors, values about 25 are cause for concern. In smaller samples, (N=100) and with fewer predictors (namely three) values greater than 15 are problematic, and in very small samples (N=30) with only two predictors values greater than 11 should be examined.
- 24Mean SquaresA measure of average variability. For every sum of squares (which measure the total variability) it is possible to create mean square by dividing by the number of things used to calculate the sum of squares (or some function of it).
- 25Model Sum of SquaresA measure of the total amount of variability for which a model can account. It is the difference between the total sum of squares and residual sum of squares.
- 26MulticollinearityA situation in which two or more variables are very closely linearly related.
- 27Multiple rThe multiple correlation coefficient. It is the correlation between the observed values of an outcome and the values of the outcome predicted by a multiple regression model.
- 28Multiple RegressionA extension of simple regression in which an outcome is predicted by a linear combination of two or more predictor variables.
- 29Ordinary Least Squared (OLS)A method of regression in which the parameters of the model are estimated using the method of least squares.
- 30Outcome VariableA variables whose values we are trying to predict from one or more predictor variables.
- 31Perfect CollinearityExists when at least one predictor in a regression model is a perfect linear combination of the others (the simplest example being two predictors that are perfectly correlated-- they have a correlation coefficient of 1).
- 32Predicted ValueThe value of an outcome variable based on specific values of the predictor variable or variables being placed into a statistical model.
- 33Predictor VariableA variable that is used to try to predict values of another known as an outcome variable.
- 34ResidualThe differences between the value a model predicts and the values observed in the data on which the model is based. Basically, an error. When the residual is calculated for each observation in a data set the resulting collection is referred to as the residuals.
- 35Residual Sum of SquaresA measure of the variability that cannot be explained by the model fitted to the data. It is the total squared deviance between the observations, and the value of those observations predicted by whatever model is fitted to the data.
- 36ShrinkageThe loss of predictive power of a regression model it the model had been derived from the population from which the sample was taken, rather than the sample itself.
- 37Simple RegressionA linear model in which one variable or outcome is predicted from a single predictor variable.
- 38Standardized DFBetaA standardized version of BFBeta. These standardized values are easier to use than DFBeta because universal cut-off points can be applied. Stevens (2002) suggests looking at cases with absolute values greater than 2.
- 39Standardized DFFitA standardized version of DFFit
- 40Standardized ResidualsThe residuals of model expressed in standard deviation units. Standardized residuals with an absolute value greater than 3.29 (actually, we usually just use 3) are cause for concern because in an average sample a value this high is unlikely to happen by chance; if more than 1% of our observations have standardized residuals with an absolute value greater than 2.58 (we usually just sat 2.5) there is evidence that the level of error within our model is unacceptable (the model is a fairly poor fit of the sample data); and if more than 5% of observation have standardized residuals greater than 1.96 (or 2 for convenience) then there is also evidence that the model is a poor representation of the actual data.
- 41Stepwise RegressionA method of multiple regression in which variables are entered into the model based on statistical criterion (the semi-partial correlation with the outcome variable). Once a new variable is entered into the model, all variables in the model are assessed to see whether they should be removed.
- 42Studentized Deleted ResidualsA measure of the influence of a particular case of data. This is a standardized version of the deleted residual.
- 43Studentized ResidualsA variation on standardized residuals. A studentized residual is an unstandardized residual divided by an estimate of its standard deviation that varies point by point. These residuals have the same properties as the standardized residuals but usually provide more precise estimate of the error variance of a specific case.
- 44Suppressor EffectsSituation where a predictor has a significant effect, but only when another variable is held constant.
- 45t-StatisticStudent's t is a test statistic with a known probability distribution (the t-distribution). In the context of regression it is used to test whether a regression coefficient b is significantly different from zero; in the context of experimental work it is used to test whether the differences between two means are significantly different from zero.
- 46ToleranceTolerance statistics measure multicollinearity and are simply the reciprocal of the variance inflation factor (1/VIF). Values below 0.1 indicates serious problems, although Menard (1995) suggests that values below 0.2 are worthy of concern.
- 47Total Sum of SquaresA measure of the total variability within a set of observations. it is the total squared deviance between each observation and the overall mean of all observations.
- 48Unstandardized ResidualsThe residuals of a model expressed in the units in which the original outcome variable was measured.
- 49Variance Inflation Factor (VIF)A measure of multicollinearity. The VIF indicates whether a predictor has a strong linear relationship with the other predictor(s). Myers (1990) suggests that a value of 10 is a good values at which to worry. Bowerman and O'Connell (1990) suggests that if the average VIF is greater than 1, then multicollinearity may be biasing the regression model.
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- Psychology Flashcards on Stats Chap 8, created by Sarah Church on 07/10/2016.
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