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Research Methods
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- 1What is Multiple Regression?Evaluates the relationship between
1 CONTINUOUS DV
and 2 or more IVs
• y= mx1 + mx2 + b - 2Describe Standard Multiple Regression(forced entry)
Researcher selects IVs, all entered in one step and retained in a single model - 3Describe Hierarchical Multiple Regression(blockwise entry)
Researcher selects blocks (a block contains at least one IV), and enters the blocks in a sequence determined by theory - 4Describe Step Wise Multiple RegressionResearcher selects lists of IVs, SPSS determines which IVs make the final model based on criteria (e.g., p<0.05).
- 5MR: What are key pieces of output in the overall model?[R, R2, Adjusted R2]
(1) R = can be thought of as the relationship between the IVs (collectively) and the DV. This is the correlation between the predicated and actual scores on the DV.
(2) R2= can be thought of as the variance in the DV explained by the IVs combined.
(3) Adjusted R2= 2 is an estimate of R2 in the population. Adjusting for sample size, number of predictors. - 6MR: What are the key pieces of output as individual predictors?[b, β, r, sr2]
(1) B‐weight (B)= unstandardised coefficient, useful for predicting scores on the DV
(2) Beta‐weight (beta)= standardised coefficient, useful for assessing relative importance of IVs for prediction.
• Standardised versions of b‐weights.
•Allows comparisons of relative importance of IVs for prediction.
(3) Zero‐order correlation (r): Pearson’s correlation • Ignoring the fact that some of this relationship may also overlap with other IVs.
(4) Semi‐partial correlation (sr2): Unique relationship between IV and DV, controlling for other IVs in the model.
•This indicates the unique variance the IV contributes to the DV. - 7Assumptions in Multiple Regression(1) Assumption Outliers:
•Standardised residuals smaller than ‐3.29 or greater than +3.39 (our cut‐off for outliers in the solution).
(2) Case wise statistics:
•cooks distance = more than > 1 indicates a case is exerting undue influence on the model.
•leverage value = greater than 3*(k‐1)\n are problematic
(3) Assumption Multicollinearity:
•is a condition in which the independent variables are highly correlated (r=0.8 or greater) such that the effects of the independents on the outcome variable cannot be separated
(4) Assumption of Normality:
•Look at K test sig value lower than .001 (bad); sig value greater than .001(good).
K‐S test is influenced by the large sample size.
(5) Assumption Homoscedasticity:
•Points should be distributed evenly above and below 0. •Assumption has been met if most cases are within the bounds of ‐2 and +2 standardised residuals.
(6) Assumption Independence of Errors:
•Durbin‐Watson tests the serial (or auto‐) correlation between residuals for adjacent cases in dataset.
• Within bounds of 1‐3
• 0‐1 indicates Type 1 Error - 8What is a reference category?A 'reference' category is so named and identified as a category of comparison for the other categories. In other words, the other categories are compared to the reference. By default R uses the alpha-numerically first category as the reference category
- 9Key assumptions of Logistic Regression(1) Independent Errors
(2) Multicollinearity and Singularity
• Correlations between predictor variables
• Tetrachoric correlations for binary variables
• Pearson’s correlation of continuous variables
(3) Linearity between continuous IVs & log of DV
• Linearity between continuous predictors or IVs and the log of the DV
• Scatter plot
• Examine line of best fit
(4) Outliers
• Are their extreme cases which could be influential
• Cooks distance & Standardised residual
• Produced as SPSS output
• Remove or transform
(5) Sufficient data
• Use a contingency table to check
• Collect more data (at least 5 per cell) or collapse levels of IV - 10What does the b weight represent in logistic regression?b weight = b = change in (log odds) of Y = 1 for 1 unit change in IV
- 11What is an Odd Ratio ?Odds Ratio (OR) is a measure of association between exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
- 12How do we interpret Odd Ratio?OR = change in likelihood of Y = 1 for 1 unit change in IV
OR < 1 means Y = 1 is less likely for target level of IV
OR > 1 means Y = 1 is more likely for target level of IV
OR = 1 means no difference between groups
OR = (odds for target group) / (odds for reference group)
Odds ratio, OR = exp(B) - 13When should logistic regression be used?When DV is categorical and used to predict the outcome such as group membership.
IV can be categorical or continuous - 14What is logistic function? How does it differ from other functions?a mathematical way of explaining the shape of line of best fit - its a common 'S' shape - puts a limit on growth
Linear Function = straight line
Quadratic Function = U shape - 15What is moderation in statistical analysis?moderation = testing whether the association of one variable with another is influenced by a third variable.
- it examines the way one variable/modifies/moderates an association - 16When should you use a MODERATION analysis?when the effect of the IV on the DV depends on the values of another IV(moderator)
- 17Explain how you would undertake a MODERATION analysis.Rather than testing a causal link between these other variables, moderation tests for when or under what conditions an effect occurs. Moderators can strength, weaken, or reverse the nature of a relationship.
- 18What is MEDIATION in statistical analysis?Tests a causal pathway a -> b -> c
- 19When should you use a MEDIATION analysis?Mediation tests whether the effects of X (the independent variable) on Y (the dependent variable) operate through a third variable, M (the mediator).
-when you want to see if the effect of something on something is because something else - 20How to interpret MEDIATION outputIf the mediation effect is strong, then the remaining relationship between the IV and DV should be small and close to zero
- 21What are key steps in MEDIATION analysis?the key steps in the analysis are:
(1) to establish that the preconditions for mediation are met (bivariate correlations will establish this)
(2) test the mediation effect for significance (covered by PROCESS)
(3) evaluate the effect size for this mediation effect (also covered by PROCESS). - 22What is structural equation modelling (SEM)?- a way to analyse associations between variables
- umbrella term for a range of analyses:
(1) path analyses (structural relationships - which variables are related)
(2) factor analysis (measurement model - how to measure these variables)
(3) path + factor analysis - 23How does path analysis fit within SEM?Path analysis is a form of multiple regression statistical analysis that is used to evaluate causal models by examining the relationships between a dependent variable and two or more independent variables
- 24What are the basic building blocks of SEM?(1) squares/rectangles = reflect measured variables (quantities that are measured and exist in your data set) they have mean and variance
(2) circles = reflect latent variables (quantities that are implied by my model) could mean an underlying variable
(3) error term = variance unexplained in a DV by predictors in the model
(4) arrows = connect variables in model - 25How is SEM (in particular, path analysis) different from multiple regression?regression: one DV at a time & no need to make assumptions about whether predictors relate to each-other.
SEM: multiple DV in same model. variable can be both IV and DV at the same time. need to explicitly state which variables relate to each other (via arrows) - 26What are the advantages of path analysis?The principal advantage of path analysis is that it allows the researcher to estimate the relative influence of variables within a causal network
- 27Explain how to evaluate your model using the chi-square statistic.chi square: it is tested for significance... we want p > .05 = our model is not rejected -we test model chi square (default model in AMOS) against the saturated model -global fit
- 28What is Factor Analysis?a data reduction method.
We reduce a large number of variables to a small number of factors (latent variables). These factors explain variance in the variables and correlations among these variable - 29What is the assumption to be tested in Factor Analysis?The associations between these variables is due to a shared underlying factor
- 30What does a Confirmatory factor analysis imply?Confirmatory approach indicates variables and tell AMOS how the variables go together • Focus is on separating shared from unique variance
- 31Scaling-Scaling the error terms to 1 ensures that variance explained by the factor + variance in the error term = 1
-Take home message:
1. Model won’t run until you scale the latent variables.
2. Set a factor loading to 1, and all error term regression weights to 1. - 32What are some problems with chi-square?• Favours complexity / model over‐fitting
• Sensitive to non‐normality – more likely to reject our model.
• Sensitive to sample size – harder to achieve p > .05 with larger samples
• Sensitive to size of correlations – model fit punished more by omission of big correlations than small.
• Sensitive to measurement error – measurement error reduces power by reducing possible size of correlations; bias is in favour of accepting your model. - 33Alternative fit indices beyond chi-square in Factor Analysis(1) SRMR= standardised root mean residual.
Values range from 0 to 1, closer to zero preferred
(2) RMSEA= root mean square error approximation
Values range from 0 to 1, closer to 1 preferred
(3) CFI = • Comparative fit index (CFI)
CFI > .95 for good fitting model (>.90 minimally acceptable*)
(4)TLI= • Tucker Lewis Index
Note: we typically report CFI or TLI, not both - 34SEM vs PATH ANALYSISSEM: separates out noise from variance we are interested in
PATH ANALYSIS: lumps noise and variance of interest together - 35Explain identification in SEM(1) Just‐identified model: all degrees of freedom used
(2) Over‐identified model: we have degrees of freedom remaining.
(3) Under‐identified model: we have insufficient degrees of freedom (AMOS wont run, simplify model) - 36What to do when you have a poor fitting model?Redifine model via:
(1) Model Building
(2) Model trimming
(3) Model comparison
(4) look at Modification Indices (the lower the better) - 37How to compare nested vs non-nested models?(1) Nested: via Likelihood Ratio Test, which compares the chi square values - Can also compare in terms of variance explained in DVs, redundancy of paths (any non‐sig paths?), and model complexity.
(2) Non-nested (if different variables are introduced) via Bayesian Information Criterion (BIC) lower value = better fitting - 38What is Multilevel Modelling (MLM)?A flexible framework to model relationships between variables in situations where data are clustered.
- 39MLM. What is clustering?Cluster analysis is a multivariate method which aims to classify a sample of subjects (or ob- jects) on the basis of a set of measured variables into a number of different groups such that similar subjects are placed in the same group.
- 40MLM. What is Intra class correlations?Intra-class correlations (ICCs):
test for cluster differences on DV (random intercept); significance testing of random effects for Level 1 relationship (random slope) tests need for random effects - 41MLM. What is 'centring'?Centring of Level 1 predictors is a way to separate within‐ from between‐cluster variance in the IV. Leads to 2 questions for a Level 1 relationship: (Within clusters) What is the relationship between time spent studying and performance? (Between clusters) What is the relationship between class average time spent studying and average class performance?
-Typically best to use group‐mean centring for Level 1 predictors
=use grand mean centring for level 2 predictors - 42MLM. Level 1 Centring- variables have two key sources of variance: within cluster and between cluster.
-Typically best to use group‐mean centring
-random slope: if you have one or more Level 1 predictors, you need to check for each (it’s an empirical question!).
-If p < .05, retain fixed slope and random slope
-If p > .05, just retain fixed slope (one slope is sufficient for all groups). - 43MLM. Level 2 Centring- there is only one source of variance as predictor variance can’t be split further into groups – can still centre, but in different way (grand mean centring).
- no random slope if you only have level 2 predictors - 44MLM. Random Effects-parameter (intercept or slope) varies across group
-MLM allows for fixed and random effects
-MR forces effects to be fixed
-sometimes we need both fixed and random effects in hierarchical datasets - 45MLM. Fixed Effects-parameter (intercept or slope) is consistent across clusters.
-Can also think of the fixed effect as the average effect across all clusters
-Sometimes, the fixed effect will be sufficient because although we have different clusters, the relationship of interest is roughly the same magnitude across clusters - 46What is FACTOR ANALYSIS?a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.
- 47FA. What are dimensions?Dimensionality = number of variables (k)
• Each variable in a set of data contributes a dimension to the analysis.
• Each dimension is uncorrelated to each other dimension - 48FA. What are Eigenvectors?direction of the relationship (correlation between multiple variables)
- 49FA. What are Eigenvalues?eigenvector has an amount of variance (correlation between multiple variables) total eigenvalue = number of variables... eigenvalue bigger than 1 are better than average
- 50What are basic requirements for a Factor Analysis?(1) minimum of 300 cases
(2) Missing data must be addressed prior to analysis
(3) meet all assumptions - 51How do we asses if Factor Analysis has worked?non- significant and chi-square close to 1
- 52What are rotations in Factor Analysis?Rotations minimise the complexity of the factor loadings to make the structure simpler to interpret
- 53FA: Orthogonal Rotation-Factors will not be related
-Unrealistic in many situations
-via: Quartimax, Varimax, Equemax - 54FA: Oblique Rotation--Allows factors to be correlated
-Realistic assessment of data in the wild
-via: Oblimin, Promax - 55What is MANOVA?MANOVA is an extension of ANOVA &
• MANOVA is an extension of Factor Analysis
• In MANOVA, we find the difference in MEANs for many DVs because of your membership of a group, or groups based on a single variable.
used by researchers wanting to understand treatment. - 56MANOVA. type 1 & type 2 errorType I error (α): where we conclude a score is so extreme that it must have come from the alternate distribution when the alternate is false
Type II error (β): is the probability of finding scores so low we conclude they come from the null distribution when the null is false - 57MANOVA participantsNumber of participants depends upon how much design power you have • Power depends upon type 1/type 2 error
Power is 1‐ β - 58MANOVA power= the ability of a test to correctly reject a false hypothesis
Power is 1‐ β - 59How to interpret MANOVA?(1) Box test = Checks assumption about the homogeneity of variance‐covariance.
non sig = no violation
(2)multivariate test table = tells what results we got and how significant they were, as well as telling us about the effect sizes
(3) Wilk’s Lambda (λ) measures of the relative size of the error
– Ranges 0 to 1, 1: no difference,
0: large difference
• Multiplies all eigenvectors & divides by multiplication of variance
– As the effect gets bigger, Wilk’s Lambda decreases.
– Use when ALL assumptions are met - 60How to evaluate significance of MANOVA?(1) Pillai’s Trace- Use:
• when sample size is small • where Box’s M is significant & cells with smaller n have larger variances
(2) Hotelling’s Trace- Use:
when assumptions are violated
(3) Roy’s largest root- Use:
when assumptions are badly violated - 61What is a MANCOVA?MANCOVA is when we control for a variable while doing MANOVA
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- Fichas sobre Research Methods, creado por Gabriela Morell el 19/02/2020.
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