Regression Analysis Module 1
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Questions and Answers

What is the purpose of maximizing SS Regression in a regression analysis?

  • To ignore the effects of independent variables
  • To minimize the variance in the outcome variable
  • To explain significant variation in the outcome variable (correct)
  • To reduce the predictive power of the model

    • What does the R2 coefficient represent in a regression model?

  • The correlation between the dependent and independent variables
  • The significance of the regression model
  • The proportion of variance in the dependent variable explained by the independent variables (correct)
  • The proportion of variance in the outcome variable not explained by the independent variables

    • What is the purpose of standardizing coefficients in a regression model?

  • To calculate the R2 coefficient
  • To minimize the SS Error
  • To compare the coefficients of different independent variables (correct)
  • To ignore the effects of shared variance

    • What does the semi-partial correlation measure in a regression model?

    <p>The unique contribution of a specific independent variable to the dependent variable</p> Signup and view all the answers

    What is the purpose of regression diagnostics?

    <p>To ensure an accurate relationship between predictors and outcome</p> Signup and view all the answers

    What is an outlier score in a regression analysis?

    <p>A score that is significantly different from other scores</p> Signup and view all the answers

    What is the purpose of studentized residuals in a regression analysis?

    <p>To detect unusual scores in the data</p> Signup and view all the answers

    What is partial correlation in a regression model?

    <p>The relationship between two variables while controlling for other variables</p> Signup and view all the answers

    What is the main purpose of Cook's Distance?

    <p>To measure the influence of a data point on the regression slope.</p> Signup and view all the answers

    What is the reason for excluding a data point from the analysis?

    <p>The data point influences the way the outcome of the analysis is interpreted.</p> Signup and view all the answers

    What does a high score on Cook's Distance indicate?

    <p>A data point has an inconsistent pattern of responses for the predictor variables and the outcome variable.</p> Signup and view all the answers

    What is the purpose of a semi-partial correlation?

    <p>To measure the correlation between a predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.</p> Signup and view all the answers

    What is the definition of leverage?

    <p>A measure of the distance between a data point and the regression line.</p> Signup and view all the answers

    Why may there be a significant association in an IV and DV in Pearson's Correlation, but not in multiple regression analysis?

    <p>Because Pearson's Correlation does not control for the variance shared between other predictors.</p> Signup and view all the answers

    What does a standardized regression coefficient provide?

    <p>The relative magnitude of effects found among predictors.</p> Signup and view all the answers

    What is the main assumption of regression?

    <p>Linearity, normality, homogeneity, and independence of observations.</p> Signup and view all the answers

    What is the purpose of the Mahalanobis distance?

    <p>To identify outliers in a dataset.</p> Signup and view all the answers

    What happens to the sum of squares (SSregression) when the predicted inattention scores vary widely?

    <p>It increases.</p> Signup and view all the answers

    What is the reason for the uniquely explained variance being small in the model?

    <p>There were high correlations between boredom and other predictor variables in the model.</p> Signup and view all the answers

    What is the purpose of entering IVs in a specific order in hierarchical regression?

    <p>To determine the causal priority of the predictor variables.</p> Signup and view all the answers

    What is the purpose of using tolerance in regression analysis?

    <p>To measure the part of the IV not accounted for by other IVs.</p> Signup and view all the answers

    What is the advantage of using standard multiple regression?

    <p>The combination of predictors together explain a significant amount of variance in the outcome variable.</p> Signup and view all the answers

    What is multicollinearity, and what problem does it cause in regression models?

    <p>It is when IVs have high correlations with each other, causing statistical errors.</p> Signup and view all the answers

    What is the purpose of using R squared change in hierarchical regression?

    <p>To determine how much each IV adds to the explanation.</p> Signup and view all the answers

    Why is it important to enter IVs in a specific order in hierarchical regression?

    <p>To determine the causal priority of the predictor variables.</p> Signup and view all the answers

    What is the difference between hierarchical regression and statistical regression?

    <p>Hierarchical regression is theory-driven, while statistical regression is data-driven.</p> Signup and view all the answers

    What is the purpose of using variance inflation factor (VIF) in regression analysis?

    <p>To detect multicollinearity problems in the model.</p> Signup and view all the answers

    What is the advantage of using hierarchical regression?

    <p>It allows researchers to explain the contribution of different IVs to the DV in a theory-driven way.</p> Signup and view all the answers

    What is the primary reason why the Sobel Test is not recommended?

    <p>It is too conservative and fails to detect significant relationships</p> Signup and view all the answers

    What is the purpose of a factor loading in Principal Components Analysis?

    <p>To reflect the strength of the relationship between each item and factor</p> Signup and view all the answers

    What is the goal of factor rotation in Principal Components Analysis?

    <p>To make the components independent and more interpretable</p> Signup and view all the answers

    What is the characteristic of components after an orthogonal rotation?

    <p>They are independent and perpendicular to each other</p> Signup and view all the answers

    What is the purpose of examining the component matrix in Principal Components Analysis?

    <p>To identify the items that are highly associated with each factor</p> Signup and view all the answers

    What is the advantage of using Varimax rotation?

    <p>It rearranges the variance to make the components more interpretable</p> Signup and view all the answers

    What is the primary purpose of hierarchical model testing?

    <p>To test the importance of different constructs</p> Signup and view all the answers

    What type of effect occurs when the effect of one predictor on an outcome is explained or partially explained by a second predictor?

    <p>Mediating effect</p> Signup and view all the answers

    What is the purpose of calculating the communality (h2) in Principal Components Analysis?

    <p>To estimate the variance explained by each item</p> Signup and view all the answers

    What is the condition required for a mediator to precede the DV?

    <p>The mediator must precede the DV in time</p> Signup and view all the answers

    What is the criterion for excluding items in Principal Components Analysis?

    <p>Items with loadings less than 0.4</p> Signup and view all the answers

    What type of research is required to establish causation?

    <p>Longitudinal research</p> Signup and view all the answers

    What is the purpose of naming factors in Principal Components Analysis?

    <p>To describe the underlying structure of the data</p> Signup and view all the answers

    What is the result of an orthogonal rotation on the component matrix?

    <p>The components become independent and perpendicular to each other</p> Signup and view all the answers

    What is the purpose of Path A in the Classic Mediation model?

    <p>To test the association between the IV and mediator</p> Signup and view all the answers

    What is the condition required for a mediating effect to be significant?

    <p>Path A and Path B must be significant</p> Signup and view all the answers

    What is the formula to obtain the total effect of the mediating pathway?

    <p>Path a * Path b</p> Signup and view all the answers

    What type of effect occurs when the effect of an IV on a DV is explained by a common cause?

    <p>Spurious effect</p> Signup and view all the answers

    What is the purpose of Path C' in the Classic Mediation model?

    <p>To test the association between the mediator and DV, after controlling for the IV</p> Signup and view all the answers

    What type of data is used in cross-sectional modeling?

    <p>Cross-sectional data</p> Signup and view all the answers

    What is the purpose of Kaiser-Meyer Olkin measure of sampling adequacy?

    <p>To describe the proportion of variance that might be described by underlying factors</p> Signup and view all the answers

    What is the purpose of Bartlett's test of sphericity?

    <p>To determine whether there are factors/components in a correlation matrix</p> Signup and view all the answers

    What is the purpose of the Anti-Image Matrices?

    <p>To measure the sampling adequacy of each item</p> Signup and view all the answers

    What is the main goal of Principal Components Analysis (PCA) and Factor Analysis (FA)?

    <p>To reduce the number of items to a few manageable sets</p> Signup and view all the answers

    What does the Pattern matrix provide?

    <p>Factor loadings that are unique and exclude shared variance</p> Signup and view all the answers

    What is the purpose of reliability analysis in research?

    <p>To measure the internal consistency of components</p> Signup and view all the answers

    What is the main difference between Principal Components Analysis (PCA) and Factor Analysis (FA)?

    <p>PCA explains all the variance, while FA explains shared variance</p> Signup and view all the answers

    What is the minimum number of response options required for items in PCA/FA?

    <p>3</p> Signup and view all the answers

    What is the purpose of orthogonal rotation in Factor Analysis?

    <p>To make the factors more interpretable</p> Signup and view all the answers

    What is the purpose of inspecting item distributions?

    <p>To exclude items with correlations &lt; 0.3 with at least one other</p> Signup and view all the answers

    What is a complex item in Factor Analysis?

    <p>An item that loads highly on multiple factors</p> Signup and view all the answers

    What is the purpose of varimax rotation in Factor Analysis?

    <p>To make the factors more interpretable</p> Signup and view all the answers

    What is the internal consistency of components measured by?

    <p>Cronbach α</p> Signup and view all the answers

    What is the minimum acceptable internal consistency for research?

    <p>.7 or greater</p> Signup and view all the answers

    What is the difference between orthogonal and oblique rotation in Factor Analysis?

    <p>Orthogonal rotation assumes independent factors, while oblique rotation assumes correlated factors</p> Signup and view all the answers

    What happens if Bartlett's test of sphericity is not significant?

    <p>There are no factors present</p> Signup and view all the answers

    What is the purpose of communalities in Factor Analysis?

    <p>To determine the percentage of variance explained in each item</p> Signup and view all the answers

    What is the advantage of using Principal Components Analysis (PCA) over Factor Analysis (FA)?

    <p>PCA explains all the variance in the data, while FA explains only the shared variance</p> Signup and view all the answers

    What is the purpose of factor loadings in Factor Analysis?

    <p>To describe the composition of each factor</p> Signup and view all the answers

    What is the purpose of using Cronbach's alpha in testing internal consistency?

    <p>To evaluate the reliability of a scale</p> Signup and view all the answers

    What is the advantage of using components/factors in other analyses?

    <p>They can be saved and used in other analyses, providing a more comprehensive understanding of the data</p> Signup and view all the answers

    What is the purpose of reporting the number of items included in the final solution?

    <p>To give readers an understanding of the scope of the analysis</p> Signup and view all the answers

    What is the main difference between principal components analysis and factor analysis?

    <p>PCA analyzes all variance, while FA analyzes shared variance</p> Signup and view all the answers

    What is the purpose of using orthogonal rotation in principal components analysis?

    <p>To extract components that are independent of each other</p> Signup and view all the answers

    What is the advantage of using varimax rotation in principal components analysis?

    <p>It extracts components that are easy to interpret</p> Signup and view all the answers

    What is the purpose of using direct oblimin rotation in principal components analysis?

    <p>To extract components that are correlated with each other</p> Signup and view all the answers

    What is the advantage of using factor scores in analysis?

    <p>They provide a more comprehensive understanding of the data</p> Signup and view all the answers

    What is the purpose of reporting the percentage of variance accounted for in each component?

    <p>To give readers an understanding of the importance of each component</p> Signup and view all the answers

    What is the purpose of using Bartlett's test of sphericity?

    <p>To test the assumption that the correlations between items are sufficient for factor analysis</p> Signup and view all the answers

    What does an eigenvalue of 1 represent in a factor?

    <p>Proportion of variance accounted for in one item</p> Signup and view all the answers

    What is the role of a moderator in a statistical analysis?

    <p>A variable that influences the effect of an independent variable on a dependent variable</p> Signup and view all the answers

    What is the purpose of using covariates in an analysis?

    <p>To control for error and better explain the association between the IV and DV</p> Signup and view all the answers

    What is the difference between a mediator and a moderator?

    <p>A mediator is a pathway or chain of events, while a moderator is a conditional or dependent effect</p> Signup and view all the answers

    What happens to the total variance when a rotated factor matrix is used?

    <p>The total variance remains constant</p> Signup and view all the answers

    What does an eigenvalue of 1 represent in a factor?

    <p>One item's proportion variance</p> Signup and view all the answers

    What is the role of a moderator in a statistical analysis?

    <p>To examine the conditional effect of IV on DV</p> Signup and view all the answers

    What is the purpose of controlling for covariates in a regression analysis?

    <p>To reduce error and improve model fit</p> Signup and view all the answers

    What is the role of a mediator in a statistical analysis?

    <p>To measure the indirect effect of IV on DV</p> Signup and view all the answers

    What is the definition of a dependent variable in a regression analysis?

    <p>A variable being predicted or explained</p> Signup and view all the answers

    What is the purpose of rotating a factor matrix?

    <p>To keep the total variance constant</p> Signup and view all the answers

    What is the definition of unique variance in multiple regression?

    <p>Variance explained by a specific IV</p> Signup and view all the answers

    What is the goal of standard multiple regression?

    <p>To predict a dependent variable using two or more independent variables</p> Signup and view all the answers

    What type of regression model is used when the researcher wants to determine the importance of different constructs and test the significance of individual IVs?

    <p>Hierarchical Regression Model</p> Signup and view all the answers

    What is the purpose of using tolerance in regression analysis?

    <p>To check for multicollinearity</p> Signup and view all the answers

    What is the result of a high score on Cook's Distance?

    <p>The data point is influential</p> Signup and view all the answers

    What is the purpose of using R squared change in hierarchical regression?

    <p>To calculate the change in variance explained by each IV at each step</p> Signup and view all the answers

    What is the assumption of homoscedasticity in regression analysis?

    <p>The variance of residual is the same for any of IV</p> Signup and view all the answers

    What is the purpose of using standard multiple regression?

    <p>To predict a DV using multiple IVs simultaneously</p> Signup and view all the answers

    What is the result of multicollinearity in regression models?

    <p>The model is unstable and unreliable</p> Signup and view all the answers

    What is the purpose of using partial correlation in regression analysis?

    <p>To control for the effect of other IVs on the outcome variable</p> Signup and view all the answers

    What is the purpose of using variance inflation factor (VIF) in regression analysis?

    <p>To check for multicollinearity</p> Signup and view all the answers

    What is the goal of regression analysis?

    <p>To minimize the residual mean square</p> Signup and view all the answers

    What is the primary goal of Mediated Regression Analysis?

    <p>To examine the influence of a mediator on the relationship between the IV and DV</p> Signup and view all the answers

    What is a characteristic of a Parallel Mediator Model?

    <p>There are two or more parallel mediators in the model</p> Signup and view all the answers

    What is the purpose of bootstrapping in Mediated Regression Analysis?

    <p>To obtain the confidence interval for the indirect effect</p> Signup and view all the answers

    What is the difference between a moderator and a mediator?

    <p>A moderator is a variable that influences the relationship between the IV and DV, while a mediator is a variable that is influenced by the IV</p> Signup and view all the answers

    What is the formula to calculate the total effect of the mediating pathway?

    <p>Path c = Path c' + Path a*b</p> Signup and view all the answers

    What is the purpose of the Sobel test?

    <p>To test the significance of the indirect effect</p> Signup and view all the answers

    What is a characteristic of an Interactive Model?

    <p>The effects of the predictor variables are conditional</p> Signup and view all the answers

    What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?

    <p>To calculate the conditional effect of the moderator variable</p> Signup and view all the answers

    What is the definition of a Conditional Effect?

    <p>The effect of a predictor variable that depends on the value of another predictor variable</p> Signup and view all the answers

    What is the purpose of a Simple Slope Analysis?

    <p>To calculate the conditional effect of the moderator variable</p> Signup and view all the answers

    What is the main purpose of using variable centring in moderated regression?

    <p>To produce a mean of 0</p> Signup and view all the answers

    What is the minimum recommended sample size for conducting a power analysis in moderated regression?

    <p>150 participants</p> Signup and view all the answers

    What is the purpose of a covariate in moderated regression?

    <p>To control for extraneous variables</p> Signup and view all the answers

    What is the difference between a main effect and an interaction in factorial ANOVA?

    <p>A main effect is the influence of one IV on the DV, while an interaction is the influence of multiple IVs on the DV</p> Signup and view all the answers

    What is the purpose of an omnibus test in ANOVA?

    <p>To test for an overall experimental effect</p> Signup and view all the answers

    What is the difference between a between-subjects design and a within-subjects design in ANOVA?

    <p>A between-subjects design involves different participants in each group, while a within-subjects design involves the same participants in each group</p> Signup and view all the answers

    What is the purpose of the F-statistic in ANOVA?

    <p>To calculate the ratio of the model to its error</p> Signup and view all the answers

    What is the purpose of the degrees of freedom in ANOVA?

    <p>To determine the number of groups and participants</p> Signup and view all the answers

    What is the difference between an ordinal interaction and a disordinal interaction?

    <p>An ordinal interaction can be interpreted, while a disordinal interaction cannot be interpreted</p> Signup and view all the answers

    What is the purpose of a contrast in ANOVA?

    <p>To compare the means of specific groups</p> Signup and view all the answers

    What is the purpose of including a control variable in a regression analysis?

    <p>To control for extraneous variables and isolate the effect of the independent variable</p> Signup and view all the answers

    What is the primary difference between a moderator and a mediator?

    <p>A moderator affects the relationship between the independent and dependent variables, while a mediator is a variable that is affected by the independent variable and in turn affects the dependent variable</p> Signup and view all the answers

    What is the purpose of factor rotation in Principal Components Analysis?

    <p>To improve the interpretability of the components</p> Signup and view all the answers

    What is the purpose of calculating the communality in Principal Components Analysis?

    <p>To determine the proportion of variance not explained by the components</p> Signup and view all the answers

    What is the condition required for a mediating effect to be significant?

    <p>The indirect effect of the independent variable on the dependent variable through the mediator must be significant</p> Signup and view all the answers

    What is the purpose of using hierarchical regression?

    <p>To examine the change in R-squared when additional independent variables are added to the model</p> Signup and view all the answers

    What is the purpose of using Varimax rotation in Principal Components Analysis?

    <p>To improve the interpretability of the components</p> Signup and view all the answers

    What is the primary assumption of multiple regression?

    <p>The residuals must be normally distributed and have constant variance</p> Signup and view all the answers

    What is the primary purpose of using partial correlation in multiple regression analysis?

    <p>To examine the correlation between the dependent variable and an independent variable while controlling for other independent variables.</p> Signup and view all the answers

    Which of the following assumptions of regression is most closely related to the concept of homoscedasticity?

    <p>The variance of residual is the same for any of the independent variables.</p> Signup and view all the answers

    What is the primary advantage of using hierarchical regression over standard multiple regression?

    <p>It allows for the examination of the unique contribution of each independent variable to the dependent variable.</p> Signup and view all the answers

    What is the purpose of using standardized coefficients in multiple regression analysis?

    <p>To compare the relative importance of each independent variable.</p> Signup and view all the answers

    What is the primary purpose of using cooks distance in multiple regression analysis?

    <p>To identify influential data points.</p> Signup and view all the answers

    What is the primary advantage of using statistical regression analysis over hierarchical regression?

    <p>It is based on the size of the correlations.</p> Signup and view all the answers

    What is the primary purpose of using leverage in multiple regression analysis?

    <p>To identify influential data points.</p> Signup and view all the answers

    What is the primary purpose of using Mahalanobis distance in multiple regression analysis?

    <p>To identify multivariate outliers.</p> Signup and view all the answers

    What is the primary purpose of using variance inflation factor (VIF) in multiple regression analysis?

    <p>To check for multicollinearity between independent variables.</p> Signup and view all the answers

    What is the purpose of variable centring?

    <p>To subtract each score from the mean score</p> Signup and view all the answers

    What is the minimum sample size recommended for conducting a moderated regression?

    <p>150 participants</p> Signup and view all the answers

    What is the purpose of the omnibus test in ANOVA?

    <p>To test for the overall experimental effect</p> Signup and view all the answers

    What is the definition of a simple effect in a factorial ANOVA design?

    <p>The effect of one independent variable at a specific level of another independent variable</p> Signup and view all the answers

    What is a three-way interaction in a factorial ANOVA design?

    <p>The interaction between three independent variables</p> Signup and view all the answers

    What is an ordinal interaction in a factorial ANOVA design?

    <p>An interaction where the lines are parallel</p> Signup and view all the answers

    What is the purpose of a contrast in a factorial ANOVA design?

    <p>To compare one factor within each level of another factor</p> Signup and view all the answers

    What is the formula for the t-statistic in a t-test?

    <p>Mean difference divided by the standard error</p> Signup and view all the answers

    What is the purpose of the degrees of freedom in ANOVA?

    <p>To determine the number of groups and participants</p> Signup and view all the answers

    What is the difference between a between-groups design and a repeated-measures design in ANOVA?

    <p>Between-groups design has different participants in each group, repeated-measures design has the same participants in each group</p> Signup and view all the answers

    In Mediated Regression Analysis, what is the requirement for the mediator to precede the DV?

    <p>The mediator must precede the DV in time</p> Signup and view all the answers

    What is the purpose of Path A in the Classic Mediation model?

    <p>To determine the relationship between the IV and the mediator</p> Signup and view all the answers

    In Moderating Regression Analysis, what is the coefficient b3?

    <p>The interaction between the IV and the moderator</p> Signup and view all the answers

    What is the difference between a mediated and a moderated regression model?

    <p>A mediated model analyzes the indirect effect of the mediator, while a moderated model analyzes the conditional effect of the moderator</p> Signup and view all the answers

    What is the purpose of the parallel mediator model?

    <p>To analyze the individual influence of each mediator on the DV</p> Signup and view all the answers

    What is the formula to obtain the total effect of the mediating pathway?

    <p>Path c = Path c' - Path a*b</p> Signup and view all the answers

    What is the result of a statistically significant moderator term in Moderated Regression Analysis?

    <p>The IV is no longer independent, and the moderator influences the relationship between the IV and the DV</p> Signup and view all the answers

    What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?

    <p>To calculate the change in the DV for a one-unit change in the IV</p> Signup and view all the answers

    What is the difference between an additive and an interactive model?

    <p>An additive model assumes independent effects of the predictors, while an interactive model assumes conditional effects</p> Signup and view all the answers

    What is the purpose of the Pick-a-Point Technique in Moderated Regression Analysis?

    <p>To create a figure to describe the association between the IV and the DV</p> Signup and view all the answers

    Study Notes

    Regression Analysis

    • Variance: The goal is to maximize SS Regression and minimize SS Error.
    • Regression Coefficient (R2): Represents the proportion of variance in the dependent variable explained by independent variables, ranging from 0 (not explained) to 1 (explains all variability).
    • Standardized Coefficients (Beta): Allows comparison of different predictors, generally ranging from -1 to +1.
    • Semi-partial Correlation: Measures the unique contribution of a specific independent variable to the dependent variable, controlling for other predictors.

    Identifying Unusual Scores

    • Regression Diagnostics: Aim for an accurate relationship between predictors and outcomes.
    • Outlier Scores: Small data points can have a large influence on the solution.
    • Studentized Residual: Measures the difference between the predicted and observed scores.
    • Leverage: Measures the influence of each data point on the regression line.
    • Cook's Distance: Combines leverage and studentized residual to identify influential data points.

    Assumptions of Regression

    • Linearity: The relationship between predictors and outcomes should be linear.
    • Normality: Residuals should be normally distributed.
    • Homoscedasticity: Residuals should have constant variance.
    • Independence: Observations should be independent.

    Multiple Regression

    • Standard Multiple Regression: Used when the combination of predictors explains significant variance in the outcome variable.
    • Hierarchical Regression: Used to test theoretical models, entering predictors in a specific order based on theoretical importance.

    Mediated Regression Analysis

    • Direct Effects: The straight arrow from predictor to outcome variable.
    • Indirect Effects: The arrow from predictor to mediator to outcome variable.
    • Mediating Variables: Explain how predictor variables influence the outcome variable.
    • Fully Mediated Effects: When the predictor variable influences the outcome variable only through the mediator.

    Factors and Principal Components

    • Principal Components Analysis (PCA): Reduces a large number of items to a smaller number of components, interested in all variance.
    • Factor Analysis (FA): Interested in the common variance, what is shared among items (co-variance).
    • Orthogonal Rotation: Produces independent components, maintaining independence between components.

    Let me know if you'd like me to clarify anything!### Factor Analysis

    • Deliberate mind wandering: enjoying mind wandering, thoughts wander on purpose, becoming absorbed in pleasant fantasy, and mind wandering to cope with boredom
    • Types of mind wandering: deliberate and spontaneous

    Principal Axis Solutions

    • Uses a 2-factor solution
    • FA eigenvalues are lower than PCA because PCA uses 100% of the variance, while FA only uses shared variance
    • Scree plot is used to determine the number of factors to extract
    • Factor matrix: all 8 items have strong loadings, but item 2 has a mix, which is not desirable
    • Varimax rotation can improve the factor matrix

    Complex Items

    • Items that correlate more than 0.35 on more than one component in the rotated solution
    • May be part of a general construct only and not explanatory when searching for independent dimensions
    • Solution: exclude the item (if there is one), or if many, components are not independent; use an oblique solution to allow for correlations between components

    Oblique Rotation

    • Components are not independent; correlations between them
    • Independent (varimax) - angle = 90 degrees
    • Oblique (not independent) - each axis moves separately
    • Not independent < 90 degrees

    Pattern Matrix and Structure Matrix

    • Pattern matrix: provides factor loadings that are unique (excludes shared variance)
    • Structure matrix: factor loadings are higher than the pattern matrix and include shared variance (variance counted twice)
    • Factor correlation matrix: gives the correlation between the two matrices

    Writing Up an Oblique Solution

    • Report total % of variance accounted for
    • Describe factors using factor loadings
    • Report correlation between factors produced

    Assumptions of Analysis

    • Bartlett's test of sphericity: determines whether there are factors/components in the correlation matrix
    • Kaiser-Meyer-Olkin measure of sampling adequacy: describes the proportion of variance that might be described by underlying factors

    Distribution of Items

    • Scales suitable for PCA/FA: non-discriminating items (same score), extreme scores
    • Bartlett's test: determines whether there are factors/components in the correlation matrix
    • Kaiser-Meyer-Olkin measure of sampling adequacy: describes the proportion of variance that might be described by underlying factors

    Strategy Analysis

    • Inspect item distributions
    • Correlation matrix: exclude items with correlations < 0.3 with at least one other
    • Assess sampling adequacy
    • Determine how many components to extract
    • Remove variables that need to be discarded
    • Perform rotations

    Reliability Analysis

    • Internal consistency of components: correlation between item and component
    • Cronbach's alpha: measures the extent to which different items on a scale are measuring the same construct
    • Good reliability: does not necessarily mean the instrument is valid

    Testing Internal Consistency Factors

    • Use items with high loading on each scale
    • Reliability statistic: using Cronbach's alpha
    • Item-total statistics: Cronbach's alpha if an item is deleted, corrected item-total correlation, and squared multiple correlation

    Using Components in Other Analyses for Validity

    • Can be saved and components/factors used in other analyses - added to data file
    • Uses linear combination produced based on rotation used for each component/factor

    Reporting Results

    • Number of items included in final solution (as well as how many excluded)
    • Assumptions
    • % variance accounted for overall and how many components included in final solution
    • If orthogonal rotation, % accounted for each component
    • Use final solution (e.g., varimax), tell reader
    • Final solution based on theoretical meaningfulness of outcome, not entirely statistics
    • Table with all items on each component and loading
    • Describe each component and name it
    • Coefficient alpha (α) for each component

    Factor Analysis

    • Eigenvalue determines the percentage of variance accounted for in a factor
    • An eigenvalue of 1 equals the proportion of variance of one item

    Moderation and Mediation

    • Moderator: a conditional/dependent effect where the influence of the independent variable (IV) on the dependent variable (DV) depends on the score of the moderator
    • Example: years in education (IV), gender (moderator), and salary (DV)
    • Mediator: a pathway or chain of events where the IV influences the mediator, which in turn influences the score on the DV
    • Example: years in education (IV), beginning salary (mediator), and salary (DV)

    Covariates

    • Should be used in an analysis when you want to control for error to better explain the association between the IV and DV

    Regression Basics

    • Standard multiple regression predicts a dependent variable (DV) using two or more independent variables (IVs) simultaneously.
    • A variable is a measurable characteristic that varies (by groups, individuals, or time).
    • Dependent/Outcome Variable (DV) is the presumed effect in the analysis.
    • Independent/Explanatory Variable (IV) is the presumed cause in an analysis.
    • Control Variable/Covariate is a variable that is not studied but included in the model/analysis.

    Regression Concepts

    • Best Fitting Line: The most appropriate line showing the relationship between dependent and independent variables.
    • Residual: Deviators from the fitted line (estimated value) to the observed values (data point).
    • Error: Difference between the observed value and the true value (often unobserved).
    • Unique Variance: Variability in a DV uniquely explained by specific IV(s) in multiple regression.
    • Shared Variance: Variability in a DV explained by multiple IV(s) simultaneously in both multiple regression and Pearson's correlation.

    General Linear Model (GLM)

    • GLM: date = model + error (regression and ANOVA).

    Regression Results

    • Regression Coefficient R2: represents the proportion of the variance in the dependent variable that is explained by the independent variables in the model.
    • Ranges from 0 (not explained) to 1 (explains all variability).
    • Unstandardized coefficient: the slope of the regression line reflecting the change in the DV from one-unit change in the IV, whilst holding all other variables constant (B).
    • Standardized coefficient: the slopes of the regression line expressed in standard deviation units (generally -1 to +1); making it comparable with other standardized coefficients.
    • Semi-partial correlation (Part)sr2: Correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
    • p-value of the model: It tests whether R2 is different from 0. A value less than 0.05 shows a statistically significant relationship.

    Identifying Unusual Scores

    • Influences the way the outcome of the analysis can be interpreted.
    • Outlier Score: Studentised residual: unusual on IV.
    • Discrepancy (most instable): unusual on IV and DV.
    • Influential: unusual on IV: Mahanobalis and Leverage.

    Assumption of Regression

    • Linearity: The relationship between IV and the mean of DV is linear.
    • Homoscedasticity: The variance of residual is the same for any of IV.
    • Normality: For any fixed value of IV, DV is normally distributed.
    • Multicollinearity: Associations between predictors (0) redundant (1) independent.

    Selecting the "Best" Model

    • Goal is to minimize the residual mean square (which maximizes R2) - by comparing regression models.

    Hierarchical Regression Model

    • Hypothesis model – we determine what happens based on theory.
    • Entered into the model at different steps, based on theoretical importance or control.

    Reporting

    • R2 change = Squared semi-partial correlation.
    • How much added variance in DV explained each step.
    • Report significance of F change.
    • Change for individual IVs not always significant.

    Mediated Regression Analysis

    • Mediating variables theoretically explain how the predictor variables influence the DV (outcome).
    • The IV should precede the mediator in time, and the mediator should precede the DV.

    Moderated Regression Analysis

    • Influence of one IV on DV "changes" based on the score on the second IV.
    • The moderator variable is the IV that influences the relationship between IV and DV, such as direction or strength.
    • The IV is no longer independent; it is "conditional" on the moderator.

    ANOVA Basics

    • Are the means different?
    • Definitions and Terms:
    • T statistics: Tests whether two group means are significantly different.
    • F statistics: The ratio of the model to its error.

    Variability

    • Between conditions: Explained by our model.
    • Within conditions: Unexplained error.

    Sum of Squares

    • SS Total: Grand Mean.
    • SS between: Variance explained by our model.
    • SS within: Variance not explained by our model.

    Degrees of Freedom

    • df for SS between: k-1 (number of conditions/groups minus 1).
    • df for SS within: N-k (Number of participants minus the number of groups).
    • df SS total: N-1 (number of participants minus 1).

    Omnibus Test

    • Tests for an overall experimental effect – that the difference lies "somewhere".

    ANOVA Designs

    • Between groups: Two experimental conditions and different people are assigned to each condition.
    • Repeated measures: Two experimental conditions and the same people take part in both conditions.
    • Mixed ANOVA: Combination of repeated and independent factors.

    Factorial ANOVA

    • Factorial Designs can show interactions.
    • The impact of one independent variable (IV) ignoring the presence of any other IV included in the design.
    • Main effect: Influence of IV without regard for other IV's in the analysis.
    • Interaction: The influence of one IV on the score of DV conditional (dependent) on the other independent variable.

    Interaction Contrasts

    • Evaluated effects of two IV's for different levels of the third IV.

    Types of Interactions

    • Disordinal Interaction: Effect of one IV, differs at the level of the second IV & direction or effect differs.
    • Ordinal Interaction: Can interpret main effects (further analysis required on statistical interaction).

    Regression Basics

    • Standard multiple regression predicts a dependent variable (DV) using two or more independent variables (IVs) simultaneously.
    • A variable is a measurable characteristic that varies (by groups, individuals, or time).
    • Dependent/Outcome Variable (DV) is the presumed effect in the analysis.
    • Independent/Explanatory Variable (IV) is the presumed cause in an analysis.
    • Control Variable/Covariate is a variable that is not studied but included in the model/analysis.

    Regression Concepts

    • Best Fitting Line: The most appropriate line showing the relationship between dependent and independent variables.
    • Residual: Deviators from the fitted line (estimated value) to the observed values (data point).
    • Error: Difference between the observed value and the true value (often unobserved).
    • Unique Variance: Variability in a DV uniquely explained by specific IV(s) in multiple regression.
    • Shared Variance: Variability in a DV explained by multiple IV(s) simultaneously in both multiple regression and Pearson's correlation.

    General Linear Model (GLM)

    • GLM: date = model + error (regression and ANOVA).

    Regression Results

    • Regression Coefficient R2: represents the proportion of the variance in the dependent variable that is explained by the independent variables in the model.
    • Ranges from 0 (not explained) to 1 (explains all variability).
    • Unstandardized coefficient: the slope of the regression line reflecting the change in the DV from one-unit change in the IV, whilst holding all other variables constant (B).
    • Standardized coefficient: the slopes of the regression line expressed in standard deviation units (generally -1 to +1); making it comparable with other standardized coefficients.
    • Semi-partial correlation (Part)sr2: Correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
    • p-value of the model: It tests whether R2 is different from 0. A value less than 0.05 shows a statistically significant relationship.

    Identifying Unusual Scores

    • Influences the way the outcome of the analysis can be interpreted.
    • Outlier Score: Studentised residual: unusual on IV.
    • Discrepancy (most instable): unusual on IV and DV.
    • Influential: unusual on IV: Mahanobalis and Leverage.

    Assumption of Regression

    • Linearity: The relationship between IV and the mean of DV is linear.
    • Homoscedasticity: The variance of residual is the same for any of IV.
    • Normality: For any fixed value of IV, DV is normally distributed.
    • Multicollinearity: Associations between predictors (0) redundant (1) independent.

    Selecting the "Best" Model

    • Goal is to minimize the residual mean square (which maximizes R2) - by comparing regression models.

    Hierarchical Regression Model

    • Hypothesis model – we determine what happens based on theory.
    • Entered into the model at different steps, based on theoretical importance or control.

    Reporting

    • R2 change = Squared semi-partial correlation.
    • How much added variance in DV explained each step.
    • Report significance of F change.
    • Change for individual IVs not always significant.

    Mediated Regression Analysis

    • Mediating variables theoretically explain how the predictor variables influence the DV (outcome).
    • The IV should precede the mediator in time, and the mediator should precede the DV.

    Moderated Regression Analysis

    • Influence of one IV on DV "changes" based on the score on the second IV.
    • The moderator variable is the IV that influences the relationship between IV and DV, such as direction or strength.
    • The IV is no longer independent; it is "conditional" on the moderator.

    ANOVA Basics

    • Are the means different?
    • Definitions and Terms:
    • T statistics: Tests whether two group means are significantly different.
    • F statistics: The ratio of the model to its error.

    Variability

    • Between conditions: Explained by our model.
    • Within conditions: Unexplained error.

    Sum of Squares

    • SS Total: Grand Mean.
    • SS between: Variance explained by our model.
    • SS within: Variance not explained by our model.

    Degrees of Freedom

    • df for SS between: k-1 (number of conditions/groups minus 1).
    • df for SS within: N-k (Number of participants minus the number of groups).
    • df SS total: N-1 (number of participants minus 1).

    Omnibus Test

    • Tests for an overall experimental effect – that the difference lies "somewhere".

    ANOVA Designs

    • Between groups: Two experimental conditions and different people are assigned to each condition.
    • Repeated measures: Two experimental conditions and the same people take part in both conditions.
    • Mixed ANOVA: Combination of repeated and independent factors.

    Factorial ANOVA

    • Factorial Designs can show interactions.
    • The impact of one independent variable (IV) ignoring the presence of any other IV included in the design.
    • Main effect: Influence of IV without regard for other IV's in the analysis.
    • Interaction: The influence of one IV on the score of DV conditional (dependent) on the other independent variable.

    Interaction Contrasts

    • Evaluated effects of two IV's for different levels of the third IV.

    Types of Interactions

    • Disordinal Interaction: Effect of one IV, differs at the level of the second IV & direction or effect differs.
    • Ordinal Interaction: Can interpret main effects (further analysis required on statistical interaction).

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    Description

    Learn about regression analysis, including maximizing SS regression and minimizing SS error. Understand how R2 represents the proportion of variance explained by independent variables in the model.

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