Hierarchical linear regression and model comparison Flashcards
Define
Hierarchical multiple regression
a special form of regression analysis in which more variables are added to the model in separate steps called “blocks.” This is often done to statistically “control” for certain variables, to see whether adding variables significantly improves a model’s ability to predict the criterion variable and/or to investigate a moderating effect of a variable
Define
Nested models
refers to models where one model contains all the terms of the other, and at least one additional term
Define
Non-nested models
models where neither can be obtained from the other by the imposition of appropriate parametric restrictions or as a limit of a suitable approximation
Define
Covariates
characteristics (excluding the actual treatment) of the participants in an experiment
Define
Log likelihood (LL)
measures the goodness of fit of a statistical model to a sample of data for given values of the unknown parameters
Define
Akaike Information Criterion (AIC)
an estimator of in-sample prediction error and thereby relative quality of statistical models for a given set of data
Define
Bayesian Information Criterion (BIC)
a criterion for model selection among a finite set of models
Definition
a special form of regression analysis in which more variables are added to the model in separate steps called “blocks.” This is often done to statistically “control” for certain variables, to see whether adding variables significantly improves a model’s ability to predict the criterion variable and/or to investigate a moderating effect of a variable
Hierarchical multiple regression
Definition
refers to models where one model contains all the terms of the other, and at least one additional term
Nested models
Definition
models where neither can be obtained from the other by the imposition of appropriate parametric restrictions or as a limit of a suitable approximation
Non-nested models
Definition
characteristics (excluding the actual treatment) of the participants in an experiment
Covariates
Definition
measures the goodness of fit of a statistical model to a sample of data for given values of the unknown parameters
Log likelihood (LL)
Definition
an estimator of in-sample prediction error and thereby relative quality of statistical models for a given set of data
Akaike Information Criterion (AIC)
Definition
a criterion for model selection among a finite set of models
Bayesian Information Criterion (BIC)
What is hierarchical multiple regression useful for?
Comparing the difference in R2 will show how much the predictor(s)/covariates uniquely contribute beyond the covariates/predictor(s)
In hierarchical multiple regression, which outputs are the most useful? What do they show?
R-square change:
- R square of current model minus the R square of the previous model. Higher values indicate that the model explains more variance than the previous model
F change:
- Higher values indicate that the previous variables + additional variables have a greater effect size than the previous variables alone
Sig. F change:
- p < .05 indicates that the F change is significantly different to previous model
What is the differene between nested and non-nested models?
Nested models are models where one includes all the variables of another model
This is not true for non-nested models
True or False:
You can only run hierarchical regression on non-nested models if a large sample size was used
False
You can’t run hierarchical regression on non-nested models
When comparing models, what do we use to determine which is better?
Log likelihood (LL)
In linear models, the negative log likelihood is often the ______________
In linear models, the negative log likelihood is often the sum of squared deviations
Most models work by __________the LL
Most models work by maximising the LL
What question does log likelihood answer?
How likely is it that we would observe these data given some parameter estimate?
For example:
- How likely is it that we would observe a score of 6, if the mean is 5?
- How likely is it that we would observe a score of 10, if the mean is 5?
What do we use to compare non-nested models?
Akaike Information Criterion (AIC)
Bayesian Information Criterion (BIC)
What do AIC and BIC both measure?
Provides a penalty for more complexs model based on how many parameters it includes
True or False:
A higher AIC/BIC is always better
False
Lower scores = better, so always pick the model with the lowest AIC/BIC
