Multivariate Data Analysis - Summary

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Chapter 1

Multivariate analysis refers to all statistical techniques that simultaneously analyze multiple measurements on individuals or objects under investigation. Factor analysis identifies the structure underlying a set of variables Discriminant analysis differentiates among groups based on a set of variables.

All the variables must be random and interrelated in such ways that their different effects cannot meaningfully be interpreted separately.

Nonmetric measurement scales
Nominal scales: only to identify the object.
Ordinal scales: only to indicate the order of the values.
Metric measurement scales
Interval scales: highest level of measurement precision together with ratio scales. Only differences is that interval uses an arbitrary zero point and ratio scales include an absolute zero point. Therefore it is not possible to say that any value on an interval scale is a multiple of some other point on the scale. Ratio scales: see above.

Measurement error: is the degree to which the observed values are not representative of the “true” values. All variables used must be assumed to have some degree of measurement error.

Validity is the degree to which a measure accurately represents what it is supposed to. Reliability if the degree to which the observed variable measures the “true” value and is “error free” Thus it is the opposite of measurement error. In order to reduce measurement error the researcher may also choose to develop multivariate measurements, also know as summated scales, for which several variables are joined in a composite measure to represent a concept.

Type I error is the probability of rejecting the null hypothesis when actually true. Type II error is the probability of failing to reject the null hypothesis when it is actually false. Power if the probability of correctly rejecting the null hypothesis when it should be rejected.

| | |Reality | | | |No difference |difference | |Statistical decision |H0: no difference |1-α |Β (type II error) | | |Ha: difference |α (type 1 error) |1-β Power |

High levels of power depend on: effect size (larger effects are easier to find), alpha (as the probability of incorrectly finding significant results decreases, so is the probability of correctly finding an effect), sample size (at large samples almost every effect is significant)

Classification of multivariate techniques
Dependence technique may be defined as on in which a variable or set of variables is identified as the dependent variable to be predicted or explained by other variables known as independent variables. Interdependence technique is one in which no single variable or group of variables is defined as being independent of dependent.

Dependence techniques can be categorized by two characteristics: the number of dependent variables and the type of measurement scale.

Overview is given at pages 14/15

Guidelines for multivariate analyses and interpretation
A researcher must not only look at the statistical significance but also at the practical significance. Multicollinearity represents the degree to which any variable’s effect can be predicted or accounted for by other variables in the analysis.

Stage 1: define the research problem, objectives, and multivariate technique to be used. Stage 2: Develop the analysis plan (desired sample size, types of variables Stage 3: evaluate the assumptions underlying the multivariate technique (Statistical and conceptual assumptions must be met) Stage 4: Estimate the multivariate model and assess overall model fit. Stage 5: Interpret the variate(s).

Stage 6: validate...
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