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Summary MethodologyOverview of Multivariate methods
Overview multivariate methods
In your own words, define multivariate analysis
Analysis of multiple variables in a single relationship or set of relationships. It is a way to
convert data into knowledge. It simultaneously analyzes multiple measurements on
individuals or objects under investigation. Any analysis of more than two variables can be
loosely considered multivariate analysis.
Name the most important factors contributing to the increased application of techniques
for multivariate data analysis in the last decade
Businesses must be more profitable, react quicker and offer higher-quality products and
services and do it all with fewer people and at lower cost. Thereby the information available
for decision-making exploded in recent years and will continue to do so in the future. And the
developments of computer hardware and software help us to apply multivariate techniques.
List and describe the multivariate data analysis techniques described in this chapter.
Cite examples for which each technique is appropriate
- Principal components and common factor analysis
- Multiple regression and multiple correlation
- Multiple discriminant analysis and logistic regression
- Canonical correlation analysis
- Multivariate analysis of variance and covariance
- Conjoint analysis
- Cluster analysis
- Perceptual mapping
- Correspondence analysis
- Structural equation modeling and confirmatory factor analysis
Explain why and how the various multivariate methods can be viewed as a family
technique
Why is knowledge of measurement scales important to an understanding of multivariate
data analysis?
- The researcher must identify the measurement scale of each variable used, so that
nonmetric data are not incorrectly used as metric data, and vice versa. If the researcher
incorrectly defines this measure as metric, then it may be used inappropriately.
- The measurement scale is also critical in determining which multivariate techniques
are the most applicable to the data, with considerations made for both independent and
dependent variables. The metric or nonmetric properties of independent and dependent
variables are the determining factors in selecting the appropriate technique.
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,What are the differences between statistical and practical significance? Is one a
prerequisite for the other?
Practical significance means of assessing multivariate analysis results based on their
substantive findings rather than their statistical significance. Whereas statistical significance
determines whether the results is attributable to chance, practical significance assesses
whether the result is useful (substantial enough to warrant action) in achieving the research
objectives.
What are the implications of low statistical power? How can the power be improved if it
is deemed too low?
Power is the probability of correctly rejecting the null hypothesis when it is false; that is,
correctly finding a hypothesized relationship when it exists. Determined as a function of (1)
statistical significance level set by the researcher for a Type I error (a), (2) the sample size
used in the analysis, and (3) the effect size being examined. Power can be improved by a lager
sample size, a lower alpha or larger effect size.
Detail the model-building approach to multivariate analysis, focusing on the major
issues at each step.
1: Define the Research Problem, Objectives, and Multivariate Technique to be used.
2: Develop the Analysis Plan
3: Evaluate the Assumptions Underlying the Multivariate Technique
4: Estimate the Multivariate Model and Assess Overall Model Fit
5: Interpret the Variate(s)
6: Validate the Multivariate Model
What is multivariate analysis?
Convert data into knowledge. Large complex data converging from data to knowledge.
Multivariate analysis in statistical terms
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 analysis. Whereas
Univariate analysis = analysis of single-variable distributions, and bivariate analysis = cross-
classification, correlation, analysis of variance, and siple regression used to analyze two
variables. To be considered truly multivariate, all the variables must be random and
interrelated in such ways that their different effects cannot meaningfully be interpreted
separately.
Multivariate analysis technieken: Kennis creëren en besluitvorming verbeteren. Multivariate
analyse refereert aan alle statistische technieken die gelijktijdig meerdere metingen analyseren
over individuen of objecten.
Some basic concepts of multivariate analysis
The variate = The building block of multivariate analysis. A linear combination of variables
with empirically determined weights. The variables are specified by the researcher, whereas
the weights are determined by the multivariate technique to meet a specific objective.
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
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,differentiates between groups of observations. In factor analysis, variates are formed to best
represent the underlying structure or patterns of the variables as represented by their
intercorrelations.
Measurement Scales
Data can be classified into one of two categories (1) nonmetric – qualitative and (2) metric –
quantitative.
Nonmetric Measurement Scales
Nonmetric data = describe differences in type or kind by indicating the presence or absence of
a characteristic or property. These properties are discrete in that by having a particular feature,
all other features are excluded (if a person is male, he cannot be female). Nonmetric
measurements can be made with either a nominal or an ordinal scale.
Nominal scales = assigns numbers as a way to label or identify subjects or objects. The
numbers assigned to the objects (categories or classes) have no quantitative meaning beyond
indicating the presence or absence of the attribute or characteristic under investigation. Also
known as categorical scales. (for instance 2 = female and 1 = male). Usually demographic
attributes.
Ordinal scales = the next higher level of measurement precision. Variables can be ordered or
ranked in relation to the amount of the attribute possessed. They are nonquantitative because
they indicate only relative positions in an ordered series (for instance the levels of consumer
satisfaction, level of education). With ordinal scales you can find out the order of the values
but not the amount of difference between the values (thus you may know that product A it
better but not how much better than B).
Metric Measurement Scales
Are used when subjects fidder in amount or degree on a particular attribute.
Interval scales = provide the highest level of measurement precision, permitting nearly any
mathematical operation to be performed. The difference with ratio scales is that interval scales
(Celsius) use an arbitrary zero point, whereas ratio scales include an absolute zero point.
The impact of choice of measurement scale
- the researcher must identify the measurement scale of each variable used, so that
nonmetric data are not incorrectly used as metric data, and vice versa. If the researcher
incorrectly defines this measure as metric, then it may be used inappropriately.
- The measurement scale is also critical in determining which multivariate techniques
are the most applicable to the data, with considerations made for both independent and
dependent variables. The metric or nonmetric properties of independent and dependent
variables are the determining factors in selecting the appropriate technique.
Measurement error and multivariate measurement
= the degree to which the observed values are not representative of the true values. Thus, all
variables used in multivariate techniques must be assumed to have some degree of
measurement error.
Validity and Reliability
In assessing the degree of measurement error present in any measure, the researcher must
address two important characteristics of a measure:
3
, 1. Validity = the degree to which a measure accurately represents what it is supposed to
(measure what you want to measure)
2. Reliability = the degree to which the observed variable measures the true value and is
error free. Thus, it is the opposite of measurement error (measure what you are
supposed to measure).
Employing Multivariate Measurement
In addition to reducing measurement error by improving individual variables, the researcher
may also choose to develop multivariate measurements, also known as summated scales, for
which several variables are joined in a composite measure to represent a concept. The
objective is to avoid the use of only a single variable to represent a concept and instead to use
several variables as indicators, all representing differing facets of the concept to obtain a more
well-rounded perspective.
The impact of measurement error
De impact van measurement error en poor reliability kan niet direct gezien worden, omdat ze
embedded zijn in de geobserveerde variabelen.
Statistical significance versus statistical power
Researchers very seldom use a census. Researchers are often interested in drawing inferences
from a sample. Interpreting statistical inferences requires the researcher to specify the
acceptable levels of statistical error that results from using a sample. The most common
approach is to specify the level of Type I Error, also known as Alpha = the probability of
rejecting the null hypothesis when it is actually true – generally referred to as a false positive.
When specifying the level op Type I Error, the researcher also determines an associated error,
termed Type II Error, or Beta (B) = the probability of not rejecting the null hypothesis when it
is actually false. It is referred to as the of the statistical inference test = the probability that
statistical significance will be indicated if it is present.
Reality
No Difference Difference
H0: No 1-α Β
Statistical difference
Decision Type II error
Ha: α 1–β
Difference
Type І error Power
Power is de waarschijnlijkheid van het juist verwerpen van de nulhypothese, wanneer die
verworpen moet worden. Dit geeft de kans op succes aan in het vinden van verschillen waar
zij ook werkelijk bestaan.
Type І error en Type ІІ error zijn inversely related, als de kans op een Type І error afneemt
wordt de kans op Type ІІ error groter.
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