Flashcards
HP3101 part 2
Cards in this deck (11)
- 1Stages of regression analysis: model selection (identify correct model from full set of predictors via explanation / prediction) // predictor comparison (interpretation, establish relative importance of predictors; relative importance affected by correlated predictors including excluded)Explanation vs prediction: with prior theory or research vs statistical selection, confirm specific theory vs find most predictive model
General question: from any pair of predictors, which will be more useful? (/+ in context of given predictors) - 2Standardised b = correlation with criterion if predictors uncorrelated (this can only be interpreted keeping other variables constant, hard to do if predictors correlated) Problem with standardised b: full sample s assumed uniform to all levels of predictor -- use partial s instead?r^2 indicates predictor's contribution to total variance if predictors uncorrelated
Partial r^2 indicates importance based on specific ordering; Kruskal's suggestion to repeat with p! orderings and take average
Commonality analysis: unique contribution + common part - 3Finding single best predictor - simple r (ignores all predictors, compare with null); best predictor after accounting for effects of all other predictors (unique contribution, direct effect) - semi-partial r or standardised b; best predictor onto given subset (partial effect) - semi-partial r or standardised b, added individuallyBudescu's intuitive definition of predictor importance = contributes more to prediction of criterion than its competitor (only 1 of them would be entered @ 2^(p-2) models), @ given level of analysis (context of subset models as basis of comparison); DA uses semi-partial correlation in pairwise fashion
- 4Complete / conditional dominance may not be applied to all pairs of predictors Averaged additional contributions (semi-partial r^2, just like in Lindeman's p! ordering model) in general dominance adds up to R^2 of full model Inverse hierarchy of DA may not hold if p > 3.
- 5Assumptions of linear regression: linear parameters (vs logistic / exponential, \ variables no need linear) / independent observation (--> independent e) / s^2_e constant across any value of X / e ~ N (only serious for small samples); first critical for unbiased b \ latter 3 still critical for standard error and sigRegression diagnostics: probe violations in assumptions (non-linear relationships / non-independence of e / homoscedasticity / normality of e) + spot improbable values and other problems with data (eg distance / leverage / influence / multicollinearity)
- 6Diagnosing non-linear relationship: scatterplot of Y vs X -> regression analysis -> plot e vs X (*e magnifies departure from linearity) -> check for non-systematic trend / fit non-parametric line (loess, no linearity requirement) -> add curve or interaction term if needed -> re-fit Y vs X if neededSources of non-independence: cluster sampling (random sample of entire clusters naturally evident in population, other clusters have ~0% chance -- check intraclass correlation) / repeated observations (-- check Durbin-Watson test for significance of autocorrelation)
- 7Homoscedasticity = consistency of s^2_e around regression line across levels of X -- check ratio of max :/: min s^2 (ideally < 10); can also be corrected through transformation of Y (\ scale may not be meaningfully interpreted), alternatively weighted least squares regression if serious violationNormality of residuals = frequency of values approximate normal curve -- check histogram + skewness + kurtosis (best to be within +/-2) / Q-Q plot (expected value vs observed value of residuals / deviation vs observed value) / Shapiro-Wilks test; can also be corrected through transformation of Y
- 8Distance = observed Y - predicted Y -- check residual value (ideally < 2 * SD of residual following normality assumption) Leverage = X - other observations (between 0 to 1, average value [p+1]./.n, ideally < 2 * [p+1]./.n); tests unusual pattern between XInfluence -- check standardised DFBETAS (partial influence, measures change in b after exclusion of data, compute for each b including b_0, best < 2 ./. sqrt(n)) / Cook's distance (for large values, D_i ~ F (p+1, n-p-1), ideally < 50th percentile)
Multicollinearity -- check tolerance (1 - R^2, ideally > 0.1) / VIF (tolerance^-1) - 9F test close to 1 if no treatment effect LSD error variance estimate uses MS_res (vs s^2 from pair in t test); Scheffe test not always pairwise (best \ still useless if omnibus not significant); Bonferroni tends to overcorrect; Turkey enough for running just all pairwises SS_A includes treatment effect + errorSummed SS_A = SS_A + SS_AxB
Subject effect vs treatment effect: random (H0:: var (pi) = 0; no need post-hoc) vs fixed (H0:: a = 0)
Compound symmetry (sphericity) assumptions in repeated measures: equal var (Y) / var (e), r = rho from same subject \ r = 0 between subjects - 10Dealing with homogeneity of correlation violation: observations of same type, measured same way, never treat different quantity measures as within-subject factor even if @ same subject, take note of time-series data (far apart scores have higher correlations than adjacent)Dealing with violations of sphericity: likelihood-ratio statistic W / correct df in F test to reduce false positives (eg Huynh-Felt / Greenhouse-Geisser / conservative lower bound with E = (J-1)^-1) / multivariate analysis / do tests of contrasts (no need compound symmetry because no repeated measures)
- 11Factorial design - need insignificant interaction before going into marginal means etc Contrast analysis can be for planned or post-hoc comparisons Contrast among J = weighted sum of J means, sum of weights == 0; H0:: psi = 0; var (psi) = var (e) * SS weights ./. nOrthogonality - indicates independent contrast information; summed SS_contrast = SS_A for orthogonal sets
No more contrasts than df of omnibus for mutually orthogonal sets
Trend analysis - at most J-1; no need equal spacing \ must be orthogonal
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- Psychology Flashcards on HP3101 part 2, created by Andrew Susilo on 23/10/2022.
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