Key terms & threshold values per analysis - MMSR
General
Direct causal relationship: A leads to B (linear)
Exogenous variable: independent V: influences other variable
Arrow pointing at another variable
Endogenous variable: dependent V or mediator: influenced by other variable
Arrow pointing at them
Mediated causal relationship: A → Z → B: Z is mediator
Partial mediation: effect between A and B remains significant after
inclusion of mediator
Spurious relationship: Z influences A and B. A and B do not correlate
(example: warm weather influences ice cream
consumption and drowning)
Confound variable: impacts both IV and DV. Cause for main effect
Bidirectional causal relationship: A affects B. B affects A: not at the same time. Both DV
Unanalyzed relationship: correlation between A and B
Moderated causal relationship: M affects relation of A on B. M is moderator
Correspondence rules: translating theoretical language into observational
language
Measurement model: observational (x1, x2 etc.). How variables make the
construct
Structural model: theoretical (Greek lettering). Look at relationship
between constructs
Multi-item measurement: increases reliability and validity
Formative measurement model: items form construct. Arrow from measure to construct.
Indicators not correlated. Dropping indicator alters
meaning of construct. Connected by regression
coefficients. Used for estimating consequences.
Reflective measurement model: items reflect construct. Arrow from construct to measure.
Indicators correlate. Dropping indicator does not alter
meaning of construct. Takes measurement error into
account at item level. Check with factor analysis. Used
for testing relationships.
Reliability: dots are together, so measured the same
Validity: dots are around the target, you measure what you want
to measure
Skewness: positive= many on left, negative= many on right
(threshold= -3 to 3)
Kurtosis: steepness (positive= steep, negative= flat)
Multicollinearity: correlation between IVs. Represents the degree to which
any variable’s effect can be predicted or accounted for
by the other variables in the analysis. As multicollinearity
rises, the ability to define any variable’s effect is
diminished. The addition of irrelevant or marginally
significant variables can only increase the degree of
multicollinearity, which makes interpretation of all
variables more difficult
Homoscedasticity: the assumption that dependent variables exhibit equal
levels of variance across the range of predictor
variables. Desirable because: the variance of the
dependent variable being explained in the dependence
relationship should not be concentrated in only a limited
range of independent values. Opposite =
heteroscedasticity → mostly result of nonnormality
Linearity: correlations represent only linear associations between
variables
Uncorrelated errors: model explains as much as possible without patterns
remaining.
Dummy variable: dichotomous variable that represents one category of a
nonmetric IV (0 or 1)
Beta: importance of effect relative to the other determinants
, Univariate analysis
Skewness & kurtosis Between -3 and 3 → normally distributed
Skewness / SE skewness= between -2 and 2 → normally distributed
Kurtosis / SE kurtosis= between -2 and 2 → normally distributed
Missing data < 10% → MCAR= negligible
Test missing data by: < 5% → MCAR
Chi2 for categorical > 5% → MAR
Large sample size (>400)
(Cross table)
Chi2 for categorical < 10% → MCAR
Small sample size (<400) > 10% → MAR
(Cross table)
t-test for metric variables Significant combinations: MAR
(Separate Variance t Tests) Non-significant combinations: MCAR
Little’s MCAR test Significant: MAR
(EM Means) Non-significant: MCAR
Factor Analysis
Factor loading: correlation between variable and each factor
Communalities: indication of how well the factor represents the item
Eigenvalue: all factor loadings across all items. Represents how well
one factor represents the information contained by the
items.
Total variance explained: above .60
Content validity: face validity. Assessment of correspondence of variables.
Construct validity: Extent to which a scale accurately represents the
concept of interest.
Convergent validity: variables load on expected factors. Measures of one
construct are actually related.
Nomological validity: scale is able to predict other concepts in a theoretical
model
Discriminant validity: constructs have no loadings with all other variables.
Measures that should be unrelated are actually
unrelated.
Exploratory factor analysis: finding underlying structure for correlations. No pre-
specification of number of factors or variables.
Data driven. Generation of hypotheses.
Confirmatory factor analysis: priori ideas of underlying factors. Assess the degree to
which the data meets expected structure. Testing
hypotheses.
Principal Component Analysis: looks at total variance in data.
Unities on the diagonal of cor. matrix (all 1)
More exploratory
Common Factor Analysis: a.k.a. Principal axis factoring: factors estimated based
on common variance. Each variable has a unique part.
Identify underlying dimensions and common variance.
Commonalities on diagonal of cor. matrix (not all 1)
More confirmatory (test prior knowledge)
Orthogonal rotation: axes maintained at 90 degrees → factors not correlated → Varimax
Oblique rotation: axes not maintained at 90 degrees → factors correlated,
more context specific, less comparable to other studies
→ Oblimin
Unidimensional: variable loads only and fully (factor loading= 1) on one
factor
X2: goodness of fit
SRMR: badness of fit
Cronbach’s Alpha: consistency of scale / reliability analysis
Factor Scores: look at variables and factor loadings for each factor →
Factor Score Coefficient Matrix
Select Surrogate Variables: select for each factor the variable with highest loading →
Factor Matrix
Summated Scales: highest loadings are averaged, this score is used
instead of factor score
General
Direct causal relationship: A leads to B (linear)
Exogenous variable: independent V: influences other variable
Arrow pointing at another variable
Endogenous variable: dependent V or mediator: influenced by other variable
Arrow pointing at them
Mediated causal relationship: A → Z → B: Z is mediator
Partial mediation: effect between A and B remains significant after
inclusion of mediator
Spurious relationship: Z influences A and B. A and B do not correlate
(example: warm weather influences ice cream
consumption and drowning)
Confound variable: impacts both IV and DV. Cause for main effect
Bidirectional causal relationship: A affects B. B affects A: not at the same time. Both DV
Unanalyzed relationship: correlation between A and B
Moderated causal relationship: M affects relation of A on B. M is moderator
Correspondence rules: translating theoretical language into observational
language
Measurement model: observational (x1, x2 etc.). How variables make the
construct
Structural model: theoretical (Greek lettering). Look at relationship
between constructs
Multi-item measurement: increases reliability and validity
Formative measurement model: items form construct. Arrow from measure to construct.
Indicators not correlated. Dropping indicator alters
meaning of construct. Connected by regression
coefficients. Used for estimating consequences.
Reflective measurement model: items reflect construct. Arrow from construct to measure.
Indicators correlate. Dropping indicator does not alter
meaning of construct. Takes measurement error into
account at item level. Check with factor analysis. Used
for testing relationships.
Reliability: dots are together, so measured the same
Validity: dots are around the target, you measure what you want
to measure
Skewness: positive= many on left, negative= many on right
(threshold= -3 to 3)
Kurtosis: steepness (positive= steep, negative= flat)
Multicollinearity: correlation between IVs. Represents the degree to which
any variable’s effect can be predicted or accounted for
by the other variables in the analysis. As multicollinearity
rises, the ability to define any variable’s effect is
diminished. The addition of irrelevant or marginally
significant variables can only increase the degree of
multicollinearity, which makes interpretation of all
variables more difficult
Homoscedasticity: the assumption that dependent variables exhibit equal
levels of variance across the range of predictor
variables. Desirable because: the variance of the
dependent variable being explained in the dependence
relationship should not be concentrated in only a limited
range of independent values. Opposite =
heteroscedasticity → mostly result of nonnormality
Linearity: correlations represent only linear associations between
variables
Uncorrelated errors: model explains as much as possible without patterns
remaining.
Dummy variable: dichotomous variable that represents one category of a
nonmetric IV (0 or 1)
Beta: importance of effect relative to the other determinants
, Univariate analysis
Skewness & kurtosis Between -3 and 3 → normally distributed
Skewness / SE skewness= between -2 and 2 → normally distributed
Kurtosis / SE kurtosis= between -2 and 2 → normally distributed
Missing data < 10% → MCAR= negligible
Test missing data by: < 5% → MCAR
Chi2 for categorical > 5% → MAR
Large sample size (>400)
(Cross table)
Chi2 for categorical < 10% → MCAR
Small sample size (<400) > 10% → MAR
(Cross table)
t-test for metric variables Significant combinations: MAR
(Separate Variance t Tests) Non-significant combinations: MCAR
Little’s MCAR test Significant: MAR
(EM Means) Non-significant: MCAR
Factor Analysis
Factor loading: correlation between variable and each factor
Communalities: indication of how well the factor represents the item
Eigenvalue: all factor loadings across all items. Represents how well
one factor represents the information contained by the
items.
Total variance explained: above .60
Content validity: face validity. Assessment of correspondence of variables.
Construct validity: Extent to which a scale accurately represents the
concept of interest.
Convergent validity: variables load on expected factors. Measures of one
construct are actually related.
Nomological validity: scale is able to predict other concepts in a theoretical
model
Discriminant validity: constructs have no loadings with all other variables.
Measures that should be unrelated are actually
unrelated.
Exploratory factor analysis: finding underlying structure for correlations. No pre-
specification of number of factors or variables.
Data driven. Generation of hypotheses.
Confirmatory factor analysis: priori ideas of underlying factors. Assess the degree to
which the data meets expected structure. Testing
hypotheses.
Principal Component Analysis: looks at total variance in data.
Unities on the diagonal of cor. matrix (all 1)
More exploratory
Common Factor Analysis: a.k.a. Principal axis factoring: factors estimated based
on common variance. Each variable has a unique part.
Identify underlying dimensions and common variance.
Commonalities on diagonal of cor. matrix (not all 1)
More confirmatory (test prior knowledge)
Orthogonal rotation: axes maintained at 90 degrees → factors not correlated → Varimax
Oblique rotation: axes not maintained at 90 degrees → factors correlated,
more context specific, less comparable to other studies
→ Oblimin
Unidimensional: variable loads only and fully (factor loading= 1) on one
factor
X2: goodness of fit
SRMR: badness of fit
Cronbach’s Alpha: consistency of scale / reliability analysis
Factor Scores: look at variables and factor loadings for each factor →
Factor Score Coefficient Matrix
Select Surrogate Variables: select for each factor the variable with highest loading →
Factor Matrix
Summated Scales: highest loadings are averaged, this score is used
instead of factor score
