Hierarchical Linear Regression and Model Comparison Flashcards
What method of model comparison did we focus on in this unit?
The difference between predictor variables of interest and other control/compounding variables. That’s called hierarchical regression. In the end the goal is the same: to adjust our model to best explain our observations based on theory.
What type of model is it when all predictor variables are treated equally and there is just one model?
A simultaneous model
What is a heirarchical regression essentially?
A series of related multiple regressions that are being compared by seeing what changes when you add to previous models
AKA model comparison
What information would you garner from looking at Model Summary table for a regression such a Hierarchical regression?
You would be interested in the
R squared
and Adjusted R squared
What information would you garner from looking at ANOVA table for a regression such a Hierarchical regression?
This table tells us whether our model has predictive utility. More specifically, whether the predictors (X) collectively account for a satistically significant proportion of variance in the Y variable.
If the p value in the ANOVA table is
What information would you garner from looking at Coefficients table for a regression such a Hierarchical regression?
In the coefficients table,
The unstandardised coefficient (B) details the role each indivdiual predictor plays in the regression model. This one indicates the predicted change in the DV associated with 1 unit change AFTER controlling for effects of all other predictors in the model.
So, say we see the unstandardised coefficient for negative affect is .5. and there is another predictor, anxiety, in the model. .5 is saying after controlling for for the EFFECTS of the anxiety, a 1 unit increase in negative affect will bring us to a predicted .5 increase in negative affect.
The standardised coefficient/beta (b) details the predicted change in SD’s in the DV associated with a 1 SD change in the relevant predictor after controlling for the effects of the remaining predictors in the model.
Finally, the t statistics and sig levels tell us whether the predictors account for a SIGNIFICANT proportion of UNIQUE variance in the DV - so unique variance is variance that cannot be explained by OTHER predictors in the model. So, say you see sig of .5 next to negative affect, you have anothe predictor (Caffeine) and DV is sleep quality. That says negative affect cannot account for variance in sleep quality BEYOND that which is already explained by caffeine.
What information would you garner from looking at Part and Partial Correlations table for a regression such a Hierarchical regression?
The Part is the semi-partial correlation. This is a really important unit as looking at it tells us that, if we were to square that unit, say part = .182 for certainty, THEN 3.3% of variance in sleep quality can be uniquely attributed by certainty.
So r squared would decrease by .182 if certainty was removed from the model.
So this is in the coefficients part
The PARTIAL correlation is just the partial correlation between the predictor and DV.
What does the Adjusted R squared figure represent in regression when looking at in ANOVA table?
Provides a more accurate estimate of the true extent of the relationship between the predictor variables and the DV. It offers a better estimate of the population r squared.
How does R squared and adjusted R squared differ?
Often referred to as SHRINKAGE. Adjusted R squared is more conservative due to the risk that regression has for overfitting the data..
What is adjusted R squared essentially saying regarding replication with the sample the population was drawn from?
If we were to replicate this study many times with samples drawn from the same population we would, on average, account fo X of the variance in DV with predictors X and X.
What is adjusted R squared essentially saying regarding replication with the sample the population was drawn from?
If we were to replicate this study many times with samples drawn from the same population we would, on average, account fo X of the variance in DV with predictors X and X.
If in a HR, the coefficient for a covariate becomes smaller or non significant, what does this show?
That the effect of the covariate, the unique variance that it accounts for regarding the DV, goes away when controlling for it.
So comparing the regression coefficients for covariates tells us how much smaller the relations are after accounting for potential confounding factors/covariates
If in a HR, the coefficient for a covariate becomes smaller or non significant, what does this show?
That the effect of the covariate, the unique variance that it accounts for regarding the DV, goes away when controlling for it.
So comparing the regression coefficients for covariates tells us how much smaller the relations are after accounting for potential confounding factors/covariates
So you have a HR ANOVA output in front of you and you want to see how each predictor variable is influencing the DV as it is added to the model. What would you look at?
R2
Why would you look at R2 change?
To see the exact amount of variance change in the model on the DV when you add the next covariate.
How would we work out which model is better - which information would we look at?
By looking at r2 change and f change (on the Model Summary)
First look at r2 change for each model - you would look at the first model to see what the change is.
If the models sum of squares (as seen in the ANOVA summary table) is much greater than the residual or error sum of squares, what does this mean?
It is a good model
If the model Total sum of squares, as seen in the ANOVA summary table, is greater than the residual, this indicates it is a good model. But what would we need to see to ensure this outcome is better than chance?
A significant P value! So less than
In terms of the F change value for the null model and the F statistic as seen on the ANOVA model 1, would we expect these F statistics to be the same?
Yes
To measure magnitude in significant variance across the models, what value do we look at?
R2 Change.
For VIF, what do you want to see for multicollinearity not being an issue?
> 10
For Tolerance, what do you want to see for multicollienarity not being an issue?
> 1.0
