Advanced Research Methods Lecture Flashcards

Flashcards covering core concepts, diagnostics, and various multivariate techniques including GLM, EFA, Mediation, Moderation, and Logistic Regression from the PYH401 Advanced Research Methods course.

Bivariate statistic

A statistic that analyzes the relationship involving just one Independent Variable (IV) and one Dependent Variable (DV).

Multivariate statistic

A statistic that analyzes multiple Independent Variables (IVs) and usually one key Dependent Variable (DV) of interest.

General linear model (GLM)

The mathematical framework for most multivariate statistics, based on the regression equation $\hat{Y} = a + b_1X_1 + b_2X_2 + b_3X_3...$

Unstandardized coefficient (b)

The slope of the regression line indicating the average number of points the criterion changes for every 1-unit change in the predictor.

Standardized coefficient (beta)

The slope of the regression line expressed in $Z$ scores ($\beta$), indicating the number of standard deviations $Y$ will change for every 1 standard deviation change in $X$.

R-squared ($R^2$)

A value that tells us the total proportion of variance in the criterion variable that is explained by the predictors taken as a set.

Squared semi-partial correlation ($sr^2$)

A statistic representing the unique contribution of a single predictor to the $R^2$, calculated as the difference between the $R^2$ with the predictor and the $R^2$ without it.

Exploratory Factor Analysis (EFA)

A family of techniques used to describe the pattern of correlations in a data set by identifying sub-groups of variables that go together psychometrically.

Eigenvalue

The amount of variance from the original data set that is consolidated or captured by a particular component or factor.

Eigenvector (Loading)

A set of weights that describe how a factor is calculated, indicating how important a given item is to that specific factor.

Orthogonal rotation

A method of rotating factor axes that keeps the factor vectors at right angles, maintaining them as completely uncorrelated.

Oblique rotation

A method of rotating factor axes that allows the factors themselves to be correlated.

KMO (Kaiser-Meyer-Olkin)

A statistic that assesses the proportion of correlations shared among multiple variables; ideally, it should be at least $0.6$ for factorability.

Bartlett's test

A test evaluating the null hypothesis that the correlation matrix is an identity matrix; a significant result indicates there are correlations among variables.

Communality

The proportion of variance in a variable that is shared with all other variables in the data set.

Principal components analysis (PCA)

A technique used to summarize the pattern of association among variables by creating linear composites that capture maximum variance.

Common factor analysis

A technique used to identify latent traits or psychological dimensions by only analyzing the shared variance (communalities) among variables.

Homoscedasticity

The assumption that the variance of the residuals remains constant across all levels of the predicted values.

Multicollinearity

A situation where predictor variables are so highly correlated with one another that one or more variables become redundant in the model.

Tolerance

A diagnostic calculated as $1 - R^2$ for predicting a variable from all other predictors; very low values indicate extreme multicollinearity.

Variance inflation factor (VIF)

A diagnostic measure indicating the amount the variances of the coefficients increase due to multicollinearity among predictors.

Cook's D

A measure of influence that combines residual value and leverage to identify cases most likely to affect the regression solution; values over $1$ are often concerning.

Suppressor variable

A variable that relates to the DV and IV in the opposite way than the IV and DV relate to each other, potentially masking the true relationship.

Bootstrapping

A robust analysis method consisting of taking many repeated samples with replacement from the data to empirically estimate the error of an estimate without assuming normality.

Mediation

A hypothesis where an intervening variable ($M$) explains the association between an independent variable ($X$) and a dependent variable ($Y$).

Moderation

A hypothesis where the relationship between two variables depends on the level of a third variable, representing an interaction effect.

Sobel test

A test used in mediation analysis to determine if the drop in the relationship between the IV and DV after controlling for the mediator is significantly different from zero.

Simple slopes

The relationship between the independent variable and the dependent variable at specific levels of the moderator, such as one standard deviation above and below the mean.

Logistic regression

A technique used to predict the probability or odds of belonging to a categorical outcome category based on one or more predictors.

Odds ratio ($Exp(B)$)

The estimate of the change in the odds of membership in the target group for a 1-unit change in the predictor.

Sensitivity

The hit rate, or the proportion of cases in the target group (e.g., having a disease) that are correctly classified as such.

Specificity

The rate of correct rejections, or the proportion of cases in the reference group (e.g., healthy) correctly classified as not having the condition.

ROC curve

A plot representing the sensitivity and specificity associated with every possible cutoff value in a logistic regression model.

Dummy coding

The process of representing a categorical variable with $k$ groups using $k-1$ dichotomous (0 or 1) variables.

ANCOVA

Analysis of Covariance; a model that tests for group differences on a DV after accounting for variance due to one or more continuous covariates.

MANOVA

Multivariate Analysis of Variance; a test for group differences on the best linear combination of several continuous dependent variables.

Wilks' Lambda

The most commonly reported general multivariate $F$ test in MANOVA, evaluating whether groups differ on some linear combination of DVs.