Summary MMSR 2023/2024
Introduction.................................................................................................................................................. 2
Lecture 1 – introduction.......................................................................................................................................2
Overview of multivariate methods.......................................................................................................................4
Examining the data..............................................................................................................................................6
..............................................................................................................................................................................9
Factor analysis............................................................................................................................................. 10
Introduction........................................................................................................................................................10
Exploratory factor analysis.................................................................................................................................11
Confirmatory factor analysis..............................................................................................................................16
Ancova........................................................................................................................................................ 18
Introduction........................................................................................................................................................18
Statistics in An(c)ova..........................................................................................................................................18
Assumptions of Anova........................................................................................................................................19
Interpretation of Anova......................................................................................................................................20
One-way Anova..................................................................................................................................................21
N-way Anova......................................................................................................................................................23
Ancova................................................................................................................................................................25
Repeated-measures anova.................................................................................................................................26
Man(c)ova..........................................................................................................................................................27
Regression analysis...................................................................................................................................... 29
Introduction........................................................................................................................................................29
Multiple regression analysis...............................................................................................................................31
Moderator..........................................................................................................................................................36
Logistic regression..............................................................................................................................................37
PLS-SEM....................................................................................................................................................... 39
Introduction........................................................................................................................................................39
Moderation/mediation......................................................................................................................................40
PLS-SEM..............................................................................................................................................................41
1
, Introduction
Lecture 1 – introduction
Definitions
Hypothesis consists of two parts: the independent variable (condition) that is not influenced by
anything else within the model, and the dependent variable (consequence) that is always
impacted by at least one other variable in the model.
Construct = phenomenon of theoretical interest. Needs to be defined in terms of their object
(what are we measuring), attribute level and the unit of analysis.
Theories = consist of several constructs.
Latent = indirectly observable construct. Examples: beliefs, intention, motivation.
Relationships between constructs
Direct causal relationship = A B
Can be linear one goes up, the other goes up.
Can be non-linear one goes up, the other goes down.
A = exogenous variable = independent variable.
B = endogenous variable = dependent variable.
Mediated causal relationship = A Z B
Z is the mediator, A influences B through Z.
Full mediation = effect of A on B is completely absorbed by Z.
Partial mediation = effect of A on B is only partly absorbed by Z.
A = exogenous variable = independent variable
B and Z = endogenous variable = dependent variable.
Moderated causal relationship.
Strength/direction of A on B depends on moderator M.
M
A B
A
Spurious relationship
Z influences A and B. Z
B
Bidirectional causal relationship
AB
AB
A leads to B, and B leads to A. Not necessarily at the same time. Often cross sectional data,
difficult from data point of view.
2
,Unanalyzed relationship
There is a correlation between A and B, but it’s not part of your model so you don’t analyze it.
Two-language concept
Language 1: theoretical language, translates in theoretical variables. Denoted with Greek letters.
Language 2: observational language, translates in observable variables. Denoted with our
alphabet.
The correspondence rules are how is corresponded between the languages.
Definition in model:
- Squares = indicators
- Circles/ovals = latent variables
- Small circle with e = (structural) error
term
Measurement model = how good do the
measures perform to predict the latent
construct.
Structural model = relationship of the
path between the constructs.
3
, Reflective versus formative measurement
Reflective (latent) = causality is from construct to the indicator
(measure). The construct is reflected by the measurement.
The indicators are expected to be correlated, and dropping one
indicator doesn’t alter the meaning of the construct.
Measurement error is taken into account at the item level.
This is similar to factor analysis.
Example: consumer research.
Formative (emerging) = causality is from indicator (measure) to the
construct. The indicators aren’t expected to be correlated. Dropping
one indicator can alter the meaning of the construct.
Within this course we mostly use
reflective measurement models, the
validity of the items is then usually
tested with a factor analysis.
Overview of multivariate methods
Multivariate analysis = all statistical techniques that simultaneously analyze multiple
measurements on individuals or objects under investigation.
Basic concepts
Variate = linear combination of variables with empirically determined weights, the building block
of multivariate analysis.
4
Introduction.................................................................................................................................................. 2
Lecture 1 – introduction.......................................................................................................................................2
Overview of multivariate methods.......................................................................................................................4
Examining the data..............................................................................................................................................6
..............................................................................................................................................................................9
Factor analysis............................................................................................................................................. 10
Introduction........................................................................................................................................................10
Exploratory factor analysis.................................................................................................................................11
Confirmatory factor analysis..............................................................................................................................16
Ancova........................................................................................................................................................ 18
Introduction........................................................................................................................................................18
Statistics in An(c)ova..........................................................................................................................................18
Assumptions of Anova........................................................................................................................................19
Interpretation of Anova......................................................................................................................................20
One-way Anova..................................................................................................................................................21
N-way Anova......................................................................................................................................................23
Ancova................................................................................................................................................................25
Repeated-measures anova.................................................................................................................................26
Man(c)ova..........................................................................................................................................................27
Regression analysis...................................................................................................................................... 29
Introduction........................................................................................................................................................29
Multiple regression analysis...............................................................................................................................31
Moderator..........................................................................................................................................................36
Logistic regression..............................................................................................................................................37
PLS-SEM....................................................................................................................................................... 39
Introduction........................................................................................................................................................39
Moderation/mediation......................................................................................................................................40
PLS-SEM..............................................................................................................................................................41
1
, Introduction
Lecture 1 – introduction
Definitions
Hypothesis consists of two parts: the independent variable (condition) that is not influenced by
anything else within the model, and the dependent variable (consequence) that is always
impacted by at least one other variable in the model.
Construct = phenomenon of theoretical interest. Needs to be defined in terms of their object
(what are we measuring), attribute level and the unit of analysis.
Theories = consist of several constructs.
Latent = indirectly observable construct. Examples: beliefs, intention, motivation.
Relationships between constructs
Direct causal relationship = A B
Can be linear one goes up, the other goes up.
Can be non-linear one goes up, the other goes down.
A = exogenous variable = independent variable.
B = endogenous variable = dependent variable.
Mediated causal relationship = A Z B
Z is the mediator, A influences B through Z.
Full mediation = effect of A on B is completely absorbed by Z.
Partial mediation = effect of A on B is only partly absorbed by Z.
A = exogenous variable = independent variable
B and Z = endogenous variable = dependent variable.
Moderated causal relationship.
Strength/direction of A on B depends on moderator M.
M
A B
A
Spurious relationship
Z influences A and B. Z
B
Bidirectional causal relationship
AB
AB
A leads to B, and B leads to A. Not necessarily at the same time. Often cross sectional data,
difficult from data point of view.
2
,Unanalyzed relationship
There is a correlation between A and B, but it’s not part of your model so you don’t analyze it.
Two-language concept
Language 1: theoretical language, translates in theoretical variables. Denoted with Greek letters.
Language 2: observational language, translates in observable variables. Denoted with our
alphabet.
The correspondence rules are how is corresponded between the languages.
Definition in model:
- Squares = indicators
- Circles/ovals = latent variables
- Small circle with e = (structural) error
term
Measurement model = how good do the
measures perform to predict the latent
construct.
Structural model = relationship of the
path between the constructs.
3
, Reflective versus formative measurement
Reflective (latent) = causality is from construct to the indicator
(measure). The construct is reflected by the measurement.
The indicators are expected to be correlated, and dropping one
indicator doesn’t alter the meaning of the construct.
Measurement error is taken into account at the item level.
This is similar to factor analysis.
Example: consumer research.
Formative (emerging) = causality is from indicator (measure) to the
construct. The indicators aren’t expected to be correlated. Dropping
one indicator can alter the meaning of the construct.
Within this course we mostly use
reflective measurement models, the
validity of the items is then usually
tested with a factor analysis.
Overview of multivariate methods
Multivariate analysis = all statistical techniques that simultaneously analyze multiple
measurements on individuals or objects under investigation.
Basic concepts
Variate = linear combination of variables with empirically determined weights, the building block
of multivariate analysis.
4
