Samenvatting Hoorcolleges MMSR
Contents
Samenvatting Hoorcolleges MMSR.........................................................................................................1
Lecture 1: Strategy & marketing research lecture...............................................................................1
Lecture information........................................................................................................................2
Literature: Hair, chapters 1, 9 (first part only to section "A simple example of”)............................5
Chapter 1: overview of multivariate methods................................................................................5
Chapter 9: structural equation modeling: an introduction...........................................................12
Lecture 2: Technique consultation: Explorative Factor Analysis........................................................13
Literature: Hair, chapters 2 and 3.................................................................................................15
Chapter 3: Exploratory Factor Analysis.........................................................................................15
Chapter 2: Examining your data....................................................................................................23
Lecture 4: Application lecture...........................................................................................................29
Chapter 10: SEM: Confirmatory Factor Analysis...........................................................................32
Lecture 5: Technique consultation (MANCOVA/ ANCOVA)...............................................................38
Brightspace questions...................................................................................................................38
Chapter 6: MANOVA: extending ANOVA.......................................................................................40
Chapter 5: Multiple Regression.....................................................................................................53
Chapter 8 Logistic regression........................................................................................................63
Discovering Statistics Field Multiple regression analysis...............................................................67
Example of the Logistic Regression...............................................................................................72
Chapter 9: SEM.............................................................................................................................76
Chapter 13: PLS-SEM....................................................................................................................78
PLS-SEM............................................................................................................................................78
Lecture 11: Technique consultation (PLS).........................................................................................86
Article Henseler (2016) “Using PLS path modeling in new technology research: updated
guidelines”....................................................................................................................................90
Lecture 13: end lecture/exam...........................................................................................................92
Lecture 1: Strategy & marketing research lecture
Modeling in Quantitative Research in Marketing and Strategy: Related Constructs
Nominal = Data are categorized into distinct, non-overlapping groups or categories that do not have
a specific order.
1
, For example: gender.
MODE
Ordinal = Data are categorized, but the categories are ordered or ranked in a meaningful way.
However, the differences between the ranks are not measurable or meaningful.
For example, economical status (high, medium, low) OR customer satisfaction (very satisfied,
not satisfied)
MEDIAN and MODE
Interval = Data are measured on a scale with equal intervals between values, but there is no true
zero point (i.e., zero does not mean "none" of the quantity being measured).
For example, temperature, 0 does not mean anything. 20 degrees is not 2x hotter than 10
degrees.
MEDIAN, MODE, MEAN
Ratio = Data are measured on a scale with equal intervals and a true zero point (zero means "none"
of the quantity being measured). This allows for meaningful ratios between values.
For example, height, weight
MEDIAN, MODE, MEAN
Median = middle number
Mode = most frequently
Mean = average
Lecture information
Understanding the nature of constructs
The relationship between them
How to make constructs operational
A theory is a proposed description, explanation or model of the manner of interaction of a set of
phenomena capable of predicting future occurrences or observations of the same kind and capable
of being tested through experiment or otherwise falsified through empirical observation.
A theory in marketing are often not that theoretical. They are the better when they are more
prohibited.
They do not explain something. They consists of constructs (concepts, phenomena, variables). They
are empirically testable or falsifiable.
We need them because the result of a certain situation can be different based on which theory you
use.
A hypothesis
- Usually consists of 2 parts: a condition and a consequence
- Each of the parts contain a construct: independent variables (condition) and the dependent
variables (consequence)
A construct is a conceptual term used to describe a phenomenon of theoretical interest. An indirectly
observable construct is called ‘latent’ for example IQ. A construct MUST be defined in terms of:
2
, - Object: customer loyalty
- Attribute: do people talk positively/ do they come back?
- Rater entity: who is it that rates the construct?
The relationship between constructs
- Direct causal relationship
o A linear effect. A is called exogenous (independent) variable, B is endogenous
(dependent) variable. (the higher A the higher B).
- Mediated causal relationship
o A influences B indirectly. There is an mediator. There can be
full mediation but also partial. Mediation is called partial if the
effect between A and B remains significant after inclusion of
the mediator. Z is called a mediator (variable) and thus
endogenous just like B.
- Spurious relationships
o A third variable influences A and B but sometimes we don’t
have it in our model. For example: both driven by temperature
(drowning and ice cream), but in data there is a correlation
between the 2.
- Bidirectional causal relationship
o A leads to B and B leads to A. does not have to be at the same time. Very difficult to
measure. You need longitudinal setup ad measure over time
to see better how they relate.
- Unanalyzed relationship
o There is a correlation between A and B, we might not see
it, detect it or are not interested but it.
- Moderated causal relationships
o The strength and or direction of the effect of A and B
depends on the level M. M is the moderator (variable). The
more you know (A) the better your result (B) but the class
attention can influence the result eventually as well (M).
they test out boundary conditions.
Example: theory of reasoned action
Action is influenced by the intention which is influenced by the norms and attitudes.
The Two-Language concept
Theoretical variables and observable variables.
Linking theory and observation
Plane of theory: Greek letters
Plane of observation: Roman letters
Correspondence letters: Greek letters
3
,Measurement model and structural model.
structural model uses Greek letters and
theoretical side.
Relationships between constructs is the
structural model.
First the measurement model and then the
structural model.
Measurement model =
The measurement model is observed variables into one construct.
Measurement model looks at the variables that create a phenomenon and thus a construct. While
the structural model looks at the relationship between the constructs (the relationship between the
phenomenon).
Structural model = Relationships between constructs is the structural model.
Multi-item measurement
Increases reliability and validity of measures. It allows measurement assessment:
- Measurement error
- Reliability
- validity
2 forms of measurement models:
- formative (emerging)
o direction of causality is from measure to construct
o no reason to expect indicators to be correlated
o based on multiple regression
4
, o typical for success factor research
o different aspects taking into account that don’t correlate
- reflective (latent)
o validity and reliability is part of this
o direction of causality is from construct to measure
o indicators expected to be correlated
o dropping an indicator from the measurement model does not alter
the meaning of the construct
o the construct determines the measure
o takes measurement error into account at the
item level
o similar to factor analysis
For example: drunkenness
Reflective: walking straight, high level of alcohol in blood (based on multi-collinearity, you want
correlation).
Formative: consumption of beer, consumption of wine, consumption of hard liquor. (you don’t want
correlations and thus no multi-collinearity).
Other variables play a role as well: gender, body mass, training.
Literature: Hair, chapters 1, 9 (first part only to section "A simple example of”)
Chapter 1: overview of multivariate methods
Multivariate analysis methods will increasingly influence not only the analytical aspects of research
but also the design and approach to data collection for decision making and problem solving. Analysis
of multiple variables in a single relationship or set of relationships.
Three converging trends:
1. Big data: Volume, Variety, Velocity, Veracity, Variability and Value.
5
, a. Volume: because of the high amount of information we have, it changes the
approaches that analysts take to address any research question.
b. Variety: different channels and social media platforms which leads to the question:
how can we incorporate hundreds of variables into the analyses? Data reduction,
variable selection (multiple regression)
c. Velocity: goes fast
d. Veracity: the quality of being true or accurate.
e. Variability and value: variability = variation in the flow of the data. Value = abundance
of data.
Problems of big data is: privacy, security, political disruption, invasive commercial strategies and social
stratification.
2. Statistical VS data mining models: 2 different approaches
a. Statistical or data models: statistical model is = The form of analysis where a specific
model is proposed, the model is then estimated and a statistical inference is made as
to its generalizability to the population through statistical tests. Statistical analysis
gives meaning to the meaningless numbers, thereby breathing life into a lifeless data.
Data models = the way data is organized, documented, and defined within a
database.
A researcher should correctly specify a model form that represents the process and perform the
analysis correctly to provide the explanation and prediction desired. Examples: Multiple regression,
MANOVA, discriminant analysis/logistic regression.
b. Data mining or algorithmic models: Data mining: the focus is not on the specified
model but the technique of explanation.
Algorithmic models: shifting the explanation of the process to prediction.
3. Causal inference: is the movement beyond statistical inference to the stronger statement of
“cause and effect” in non-experimental situations. Statistical inference is the practice of using
sampled data to draw conclusions or make predictions about a larger sample data sample or
population.
It is a shift from the statistical inference to the causal inference which results in a general
theory of causation based on the Structural Causal Model (SCM) with a key component
called the Directed Acyclic Graph (DAG). DAG is a Graphical portrayal of causal relationships
used in causal inference analysis to identify all “threats” to causal inference.
Multivariate analysis techniques are popular because they enable organizations to create knowledge
and thereby improve their decision-making. Multivariate analysis refers to all statistical techniques
that simultaneously analyze multiple measurements on individuals or objects under investigation.
Thus, any simultaneous analysis of more than two variables can be loosely considered multivariate
6
,analysis. Many multivariate techniques are extensions of univariate analysis (analysis of single-
variable distributions) and bivariate analysis (cross-classification, correlation, analysis of variance,
and simple regression used to analyze two variables).
Thus, the multivariate character lies in the multiple variates (multiple combinations of variables), and
not only in the number of variables or observations.
Basic concepts of Multivariate Analysis
The Variate
The variables are specified by the researcher whereas the weights are determined by the multivariate
technique to meet a specific objective. A variate of n weighted variables (X 1 to Xn) can be stated
mathematically as: Variate value = w1X1 + w2X2 + w3X3 + … + wnXn
where Xn is the observed variable and wn is the weight determined by the multivariate technique.
The result is a single value representing a combination of the entire set of variables that best
achieves the objective of the specific multivariate analysis.
- In multiple regression, the variate is determined in a manner that maximizes the correlation
between the multiple independent variables and the single dependent variable.
- In discriminant analysis, the variate is formed so as to create scores for each observation
that maximally differentiates between groups of observations.
- In exploratory factor analysis, variates are formed to best represent the underlying structure
or patterns of the variables as represented by their intercorrelations.
Any time a variate has two or more variables there is the potential for multicollinearity—the degree
of correlation among the variables in the variate that may result in a confusing effect in the
interpretation of the individual variables of the variate.
The alternative is to perform some form of dimensional reduction—finding combinations of the
individual variables that captures the multicollinearity among a set of variables and allows for a single
composite value representing the set of variables.
Several principles can be identified:
- Specification of the variate is critical
- Variable selection is necessary
- Researcher control is preferred
Measurement Scales
Nonmetric measurement scales
- Nonmetric measurement scales describe the differences in type or kind by indicating the
presence or absence of a characteristics or property. These measurements can be nominal
or ordinal scale.
1. Nominal – assigns numbers as a way to label or identify subjects. Male or female.
2. Ordinal – shows the next ‘higher’ level. Can be ranked in the ‘greater than’ or ‘less than’
relationship.
Metric measurement scales
- metric data are used when subjects differ in amount or degree on a particular attribute.
1. Interval – usage of arbitrary (random) zero point. (Fahrenheit and Celsius)
2. Ratio – include an absolute zero point. Weegschaal
Validity and reliability.
Validity is the degree to which a measure accurately represents what it is supposed to.
7
,Reliability is the degree to which the observed variable measures the “true” value and is “error free”.
It is the opposite of the measurement error.
Multivariate measurement
Summated scale is that multiple items will be summed or combined/ several variables are joined in a
composite measure to represent a concept.
General linear model (GLM) and Generalized linear model (GLZ). Within the single-equation form
there are two types of models, differentiated on the distribution of the dependent measure. The
general linear model (GLM) is the model underlying most of the widely used statistical techniques,
but it is limited to dependent variables with a normal distribution. For non-normal dependent
variables, we can either transform them to hopefully confirm to the normal distribution or use the
generalized linear model (GLZ or GLIM) that explicitly allows the researcher to specify the error term
distribution and thus avoid transformation of the dependent measure. While the use of maximum
likelihood estimation requires a different set of model fit measures than the GLM, they are directly
comparable and easily used in the same manner as their GLM counterparts (see Chapter 8 for an
example). We encourage researchers to consider the GLZ model when faced with research questions
that are not directly estimable by the GLM model.
Alpha (type 1 error) and Beta (type 2 error)
Type-1 is error refers to the non-acceptance of the
hypothesis that ought to be accepted, while type-2
refers to the acceptance of a hypothesis that ought
to be rejected.
Type 1 is 0.05 or 0.01 level so 5% or 1%.
Type 2 is (1 – beta) is the power.
(page 19 e book)
p-waarde ≤ ∝ Het resultaat is significant. H0
verworpen.
P-waarde ¿ ∝ Het resultaat is niet significant. H0 accepteren.
If the P is low, the H0 gotto go.
Statistical power analysis: researchers should design studies to achieve a power level of .80 at the
desired significance level. More stringent significance levels require larger samples to achieve the
desired power level. Conversely, power can be increased by choosing a less stringent alpha level (.10
instead of .05). Smaller effect sizes require larger sample sizes to achieve the desired power. An
increase in power is most likely achieved by increasing the sample size.
ANOVA: univariate analysis of variance: a statistical test used to analyze the difference between the
means of more than two groups. A one-way ANOVA uses one independent variable, while a two-way
ANOVA uses two independent variables.
8
, Types of Multivariate Techniques
Interdependence Techniques – variables are not dependent or independent sets, but all variables
are analyzed as a single set. E.g. factor analysis
- Exploratory Factor Analysis: used to analyze interrelationships among a large number of
variables and to explain these variables in terms of their common underlying dimensions
(factors). Principal components and common factor analysis: is a statistical approach.
- Cluster analysis: analytical technique for developing meaningful subgroups of individuals or
objects.
Dependence Techniques – all variables are seen as dependent or independent variables. E.g.
regression analysis
- Multiple regression and multiple correlation: research problem involves a single metric
dependent variable presumed to be related to two or more metric independent variables.
- Multivariate analysis of variance and covariance MANOVA : simultaneously explore the
relationship between several categorical independent variables (treatments) and two or
more metric dependent variables. This is an extension of univariate analysis of variance
(ANOVA). MANCOVA can be used in conjunction with MANOVA to remove (after the
experiment) the effect of any uncontrolled metric independent variables (covariates) on the
dependent variables. The procedure is similar to that involved in bivariate partial
correlation, in which the effect of a third variable is removed from the correlation.
- Structural equation modeling and confirmatory factor analysis : Structural equation modeling
(SEM) is a technique that allows separate relationships for each of a set of dependent
variables (covariance-based SEM). In a confirmatory factor analysis (CFA) the researcher can
assess the contribution of each scale item as well as incorporate how well the scale
measures the concept (reliability).
- Partial least squares structural equation modeling and confirmatory composite analysis:
(variance-based SEM)
- Canonical correlation analysis: Canonical correlation analysis can be viewed as a logical
extension of multiple regression analysis. Whereas multiple regression involves a single
dependent variable, canonical correlation involves multiple dependent variables.
- Conjoint analysis: Conjoint analysis is a dependence technique that brings new
sophistication to the evaluation of objects, such as new products, services, or ideas.
- Perceptual mapping, also known as multidimensional scaling : the objective is to transform
consumer judgments of similarity or preference (e.g., preference for stores or brands) into
distances represented in multidimensional space.
- Correspondence analysis: In its most basic form, correspondence analysis employs a
contingency table, which is the cross-tabulation of two categorical variables. It then
transforms the nonmetric data to a metric level and performs dimensional reduction (similar
to exploratory factor analysis) and perceptual mapping. Correspondence analysis provides a
multivariate representation of interdependence for nonmetric data that is not possible with
other methods.
Types of multivariate techniques:
Exploratory Factor Analysis: used to analyze interrelationships among a large number of variables
and to explain these variables in terms of their common underlying dimensions (factors).
9
Contents
Samenvatting Hoorcolleges MMSR.........................................................................................................1
Lecture 1: Strategy & marketing research lecture...............................................................................1
Lecture information........................................................................................................................2
Literature: Hair, chapters 1, 9 (first part only to section "A simple example of”)............................5
Chapter 1: overview of multivariate methods................................................................................5
Chapter 9: structural equation modeling: an introduction...........................................................12
Lecture 2: Technique consultation: Explorative Factor Analysis........................................................13
Literature: Hair, chapters 2 and 3.................................................................................................15
Chapter 3: Exploratory Factor Analysis.........................................................................................15
Chapter 2: Examining your data....................................................................................................23
Lecture 4: Application lecture...........................................................................................................29
Chapter 10: SEM: Confirmatory Factor Analysis...........................................................................32
Lecture 5: Technique consultation (MANCOVA/ ANCOVA)...............................................................38
Brightspace questions...................................................................................................................38
Chapter 6: MANOVA: extending ANOVA.......................................................................................40
Chapter 5: Multiple Regression.....................................................................................................53
Chapter 8 Logistic regression........................................................................................................63
Discovering Statistics Field Multiple regression analysis...............................................................67
Example of the Logistic Regression...............................................................................................72
Chapter 9: SEM.............................................................................................................................76
Chapter 13: PLS-SEM....................................................................................................................78
PLS-SEM............................................................................................................................................78
Lecture 11: Technique consultation (PLS).........................................................................................86
Article Henseler (2016) “Using PLS path modeling in new technology research: updated
guidelines”....................................................................................................................................90
Lecture 13: end lecture/exam...........................................................................................................92
Lecture 1: Strategy & marketing research lecture
Modeling in Quantitative Research in Marketing and Strategy: Related Constructs
Nominal = Data are categorized into distinct, non-overlapping groups or categories that do not have
a specific order.
1
, For example: gender.
MODE
Ordinal = Data are categorized, but the categories are ordered or ranked in a meaningful way.
However, the differences between the ranks are not measurable or meaningful.
For example, economical status (high, medium, low) OR customer satisfaction (very satisfied,
not satisfied)
MEDIAN and MODE
Interval = Data are measured on a scale with equal intervals between values, but there is no true
zero point (i.e., zero does not mean "none" of the quantity being measured).
For example, temperature, 0 does not mean anything. 20 degrees is not 2x hotter than 10
degrees.
MEDIAN, MODE, MEAN
Ratio = Data are measured on a scale with equal intervals and a true zero point (zero means "none"
of the quantity being measured). This allows for meaningful ratios between values.
For example, height, weight
MEDIAN, MODE, MEAN
Median = middle number
Mode = most frequently
Mean = average
Lecture information
Understanding the nature of constructs
The relationship between them
How to make constructs operational
A theory is a proposed description, explanation or model of the manner of interaction of a set of
phenomena capable of predicting future occurrences or observations of the same kind and capable
of being tested through experiment or otherwise falsified through empirical observation.
A theory in marketing are often not that theoretical. They are the better when they are more
prohibited.
They do not explain something. They consists of constructs (concepts, phenomena, variables). They
are empirically testable or falsifiable.
We need them because the result of a certain situation can be different based on which theory you
use.
A hypothesis
- Usually consists of 2 parts: a condition and a consequence
- Each of the parts contain a construct: independent variables (condition) and the dependent
variables (consequence)
A construct is a conceptual term used to describe a phenomenon of theoretical interest. An indirectly
observable construct is called ‘latent’ for example IQ. A construct MUST be defined in terms of:
2
, - Object: customer loyalty
- Attribute: do people talk positively/ do they come back?
- Rater entity: who is it that rates the construct?
The relationship between constructs
- Direct causal relationship
o A linear effect. A is called exogenous (independent) variable, B is endogenous
(dependent) variable. (the higher A the higher B).
- Mediated causal relationship
o A influences B indirectly. There is an mediator. There can be
full mediation but also partial. Mediation is called partial if the
effect between A and B remains significant after inclusion of
the mediator. Z is called a mediator (variable) and thus
endogenous just like B.
- Spurious relationships
o A third variable influences A and B but sometimes we don’t
have it in our model. For example: both driven by temperature
(drowning and ice cream), but in data there is a correlation
between the 2.
- Bidirectional causal relationship
o A leads to B and B leads to A. does not have to be at the same time. Very difficult to
measure. You need longitudinal setup ad measure over time
to see better how they relate.
- Unanalyzed relationship
o There is a correlation between A and B, we might not see
it, detect it or are not interested but it.
- Moderated causal relationships
o The strength and or direction of the effect of A and B
depends on the level M. M is the moderator (variable). The
more you know (A) the better your result (B) but the class
attention can influence the result eventually as well (M).
they test out boundary conditions.
Example: theory of reasoned action
Action is influenced by the intention which is influenced by the norms and attitudes.
The Two-Language concept
Theoretical variables and observable variables.
Linking theory and observation
Plane of theory: Greek letters
Plane of observation: Roman letters
Correspondence letters: Greek letters
3
,Measurement model and structural model.
structural model uses Greek letters and
theoretical side.
Relationships between constructs is the
structural model.
First the measurement model and then the
structural model.
Measurement model =
The measurement model is observed variables into one construct.
Measurement model looks at the variables that create a phenomenon and thus a construct. While
the structural model looks at the relationship between the constructs (the relationship between the
phenomenon).
Structural model = Relationships between constructs is the structural model.
Multi-item measurement
Increases reliability and validity of measures. It allows measurement assessment:
- Measurement error
- Reliability
- validity
2 forms of measurement models:
- formative (emerging)
o direction of causality is from measure to construct
o no reason to expect indicators to be correlated
o based on multiple regression
4
, o typical for success factor research
o different aspects taking into account that don’t correlate
- reflective (latent)
o validity and reliability is part of this
o direction of causality is from construct to measure
o indicators expected to be correlated
o dropping an indicator from the measurement model does not alter
the meaning of the construct
o the construct determines the measure
o takes measurement error into account at the
item level
o similar to factor analysis
For example: drunkenness
Reflective: walking straight, high level of alcohol in blood (based on multi-collinearity, you want
correlation).
Formative: consumption of beer, consumption of wine, consumption of hard liquor. (you don’t want
correlations and thus no multi-collinearity).
Other variables play a role as well: gender, body mass, training.
Literature: Hair, chapters 1, 9 (first part only to section "A simple example of”)
Chapter 1: overview of multivariate methods
Multivariate analysis methods will increasingly influence not only the analytical aspects of research
but also the design and approach to data collection for decision making and problem solving. Analysis
of multiple variables in a single relationship or set of relationships.
Three converging trends:
1. Big data: Volume, Variety, Velocity, Veracity, Variability and Value.
5
, a. Volume: because of the high amount of information we have, it changes the
approaches that analysts take to address any research question.
b. Variety: different channels and social media platforms which leads to the question:
how can we incorporate hundreds of variables into the analyses? Data reduction,
variable selection (multiple regression)
c. Velocity: goes fast
d. Veracity: the quality of being true or accurate.
e. Variability and value: variability = variation in the flow of the data. Value = abundance
of data.
Problems of big data is: privacy, security, political disruption, invasive commercial strategies and social
stratification.
2. Statistical VS data mining models: 2 different approaches
a. Statistical or data models: statistical model is = The form of analysis where a specific
model is proposed, the model is then estimated and a statistical inference is made as
to its generalizability to the population through statistical tests. Statistical analysis
gives meaning to the meaningless numbers, thereby breathing life into a lifeless data.
Data models = the way data is organized, documented, and defined within a
database.
A researcher should correctly specify a model form that represents the process and perform the
analysis correctly to provide the explanation and prediction desired. Examples: Multiple regression,
MANOVA, discriminant analysis/logistic regression.
b. Data mining or algorithmic models: Data mining: the focus is not on the specified
model but the technique of explanation.
Algorithmic models: shifting the explanation of the process to prediction.
3. Causal inference: is the movement beyond statistical inference to the stronger statement of
“cause and effect” in non-experimental situations. Statistical inference is the practice of using
sampled data to draw conclusions or make predictions about a larger sample data sample or
population.
It is a shift from the statistical inference to the causal inference which results in a general
theory of causation based on the Structural Causal Model (SCM) with a key component
called the Directed Acyclic Graph (DAG). DAG is a Graphical portrayal of causal relationships
used in causal inference analysis to identify all “threats” to causal inference.
Multivariate analysis techniques are popular because they enable organizations to create knowledge
and thereby improve their decision-making. Multivariate analysis refers to all statistical techniques
that simultaneously analyze multiple measurements on individuals or objects under investigation.
Thus, any simultaneous analysis of more than two variables can be loosely considered multivariate
6
,analysis. Many multivariate techniques are extensions of univariate analysis (analysis of single-
variable distributions) and bivariate analysis (cross-classification, correlation, analysis of variance,
and simple regression used to analyze two variables).
Thus, the multivariate character lies in the multiple variates (multiple combinations of variables), and
not only in the number of variables or observations.
Basic concepts of Multivariate Analysis
The Variate
The variables are specified by the researcher whereas the weights are determined by the multivariate
technique to meet a specific objective. A variate of n weighted variables (X 1 to Xn) can be stated
mathematically as: Variate value = w1X1 + w2X2 + w3X3 + … + wnXn
where Xn is the observed variable and wn is the weight determined by the multivariate technique.
The result is a single value representing a combination of the entire set of variables that best
achieves the objective of the specific multivariate analysis.
- In multiple regression, the variate is determined in a manner that maximizes the correlation
between the multiple independent variables and the single dependent variable.
- In discriminant analysis, the variate is formed so as to create scores for each observation
that maximally differentiates between groups of observations.
- In exploratory factor analysis, variates are formed to best represent the underlying structure
or patterns of the variables as represented by their intercorrelations.
Any time a variate has two or more variables there is the potential for multicollinearity—the degree
of correlation among the variables in the variate that may result in a confusing effect in the
interpretation of the individual variables of the variate.
The alternative is to perform some form of dimensional reduction—finding combinations of the
individual variables that captures the multicollinearity among a set of variables and allows for a single
composite value representing the set of variables.
Several principles can be identified:
- Specification of the variate is critical
- Variable selection is necessary
- Researcher control is preferred
Measurement Scales
Nonmetric measurement scales
- Nonmetric measurement scales describe the differences in type or kind by indicating the
presence or absence of a characteristics or property. These measurements can be nominal
or ordinal scale.
1. Nominal – assigns numbers as a way to label or identify subjects. Male or female.
2. Ordinal – shows the next ‘higher’ level. Can be ranked in the ‘greater than’ or ‘less than’
relationship.
Metric measurement scales
- metric data are used when subjects differ in amount or degree on a particular attribute.
1. Interval – usage of arbitrary (random) zero point. (Fahrenheit and Celsius)
2. Ratio – include an absolute zero point. Weegschaal
Validity and reliability.
Validity is the degree to which a measure accurately represents what it is supposed to.
7
,Reliability is the degree to which the observed variable measures the “true” value and is “error free”.
It is the opposite of the measurement error.
Multivariate measurement
Summated scale is that multiple items will be summed or combined/ several variables are joined in a
composite measure to represent a concept.
General linear model (GLM) and Generalized linear model (GLZ). Within the single-equation form
there are two types of models, differentiated on the distribution of the dependent measure. The
general linear model (GLM) is the model underlying most of the widely used statistical techniques,
but it is limited to dependent variables with a normal distribution. For non-normal dependent
variables, we can either transform them to hopefully confirm to the normal distribution or use the
generalized linear model (GLZ or GLIM) that explicitly allows the researcher to specify the error term
distribution and thus avoid transformation of the dependent measure. While the use of maximum
likelihood estimation requires a different set of model fit measures than the GLM, they are directly
comparable and easily used in the same manner as their GLM counterparts (see Chapter 8 for an
example). We encourage researchers to consider the GLZ model when faced with research questions
that are not directly estimable by the GLM model.
Alpha (type 1 error) and Beta (type 2 error)
Type-1 is error refers to the non-acceptance of the
hypothesis that ought to be accepted, while type-2
refers to the acceptance of a hypothesis that ought
to be rejected.
Type 1 is 0.05 or 0.01 level so 5% or 1%.
Type 2 is (1 – beta) is the power.
(page 19 e book)
p-waarde ≤ ∝ Het resultaat is significant. H0
verworpen.
P-waarde ¿ ∝ Het resultaat is niet significant. H0 accepteren.
If the P is low, the H0 gotto go.
Statistical power analysis: researchers should design studies to achieve a power level of .80 at the
desired significance level. More stringent significance levels require larger samples to achieve the
desired power level. Conversely, power can be increased by choosing a less stringent alpha level (.10
instead of .05). Smaller effect sizes require larger sample sizes to achieve the desired power. An
increase in power is most likely achieved by increasing the sample size.
ANOVA: univariate analysis of variance: a statistical test used to analyze the difference between the
means of more than two groups. A one-way ANOVA uses one independent variable, while a two-way
ANOVA uses two independent variables.
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, Types of Multivariate Techniques
Interdependence Techniques – variables are not dependent or independent sets, but all variables
are analyzed as a single set. E.g. factor analysis
- Exploratory Factor Analysis: used to analyze interrelationships among a large number of
variables and to explain these variables in terms of their common underlying dimensions
(factors). Principal components and common factor analysis: is a statistical approach.
- Cluster analysis: analytical technique for developing meaningful subgroups of individuals or
objects.
Dependence Techniques – all variables are seen as dependent or independent variables. E.g.
regression analysis
- Multiple regression and multiple correlation: research problem involves a single metric
dependent variable presumed to be related to two or more metric independent variables.
- Multivariate analysis of variance and covariance MANOVA : simultaneously explore the
relationship between several categorical independent variables (treatments) and two or
more metric dependent variables. This is an extension of univariate analysis of variance
(ANOVA). MANCOVA can be used in conjunction with MANOVA to remove (after the
experiment) the effect of any uncontrolled metric independent variables (covariates) on the
dependent variables. The procedure is similar to that involved in bivariate partial
correlation, in which the effect of a third variable is removed from the correlation.
- Structural equation modeling and confirmatory factor analysis : Structural equation modeling
(SEM) is a technique that allows separate relationships for each of a set of dependent
variables (covariance-based SEM). In a confirmatory factor analysis (CFA) the researcher can
assess the contribution of each scale item as well as incorporate how well the scale
measures the concept (reliability).
- Partial least squares structural equation modeling and confirmatory composite analysis:
(variance-based SEM)
- Canonical correlation analysis: Canonical correlation analysis can be viewed as a logical
extension of multiple regression analysis. Whereas multiple regression involves a single
dependent variable, canonical correlation involves multiple dependent variables.
- Conjoint analysis: Conjoint analysis is a dependence technique that brings new
sophistication to the evaluation of objects, such as new products, services, or ideas.
- Perceptual mapping, also known as multidimensional scaling : the objective is to transform
consumer judgments of similarity or preference (e.g., preference for stores or brands) into
distances represented in multidimensional space.
- Correspondence analysis: In its most basic form, correspondence analysis employs a
contingency table, which is the cross-tabulation of two categorical variables. It then
transforms the nonmetric data to a metric level and performs dimensional reduction (similar
to exploratory factor analysis) and perceptual mapping. Correspondence analysis provides a
multivariate representation of interdependence for nonmetric data that is not possible with
other methods.
Types of multivariate techniques:
Exploratory Factor Analysis: used to analyze interrelationships among a large number of variables
and to explain these variables in terms of their common underlying dimensions (factors).
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