Social Research Glossary   A B   Citation reference: Harvey, L., 2012-19, Social Research Glossary, Quality Research International, http://www.qualityresearchinternational.com/socialresearch/ This is a dynamic glossary and the author would welcome any e-mail suggestions for additions or amendments. Page updated 23 January, 2019 , © Lee Harvey 2012–2019. A fast-paced novel of conjecture and surprises

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Multivariate analysis (MVA)

core definition

Multivariate analysis is a statistical technique that attempts to show how more than two operationalised concepts are interrelated.

explanatory context

Introduction

Multivariate analysis (MVA) uses statistical measures of association, including correlation and regression techniques where appropriate.

MVA attempts to identify the factors that effect a specified dependent variable. It may use the patterns of association between factors (variables) to suggest psedo-causal models

MVA elaborates the measured bi-variate association (between X and Y) by takinginto account other variables. Thus MVA essentially does two things.

First, it acts as a check on the assumed relationship between X and Y as revealed by the simple bivariate correlation. Multivariate analysis is used to establish non-spurious relations through the computation of correlations between X and Y, controlling for other variables that might explain away the observed relationship. If the relationship between X & Y persists when other variables are taken into account (n-way crosstabulation; partial correlation; etc.) then the correlation is regarded as 'non-spurious', in other words, it is not a correlation that can be explained away by an antecedent or intervening variable. For example a relationship between income and education might be explained away by age.

Second, MVA acts to elaborate the association between X and Y by specifying other interrelated variables. Thus Y is seen to be associated with not a single X but a combination of variously weighted Xs.

Nonethless, this procedure is a statistical analysis that merely shows degrees of association between measured variables. Two major problems arise, first, the relationship between correlation and causality; second, the measurement of variables.

Multivariate analysis also takes into account not only the relationship of independent to dependent variables but also the interrelationship of independent variables.

When multivariate analysis is undertaken on interval scale data using techniques such as least squares regression analysis then it provides, in theory, an estimate of how much variance in a dependent variable can be attributed to variance in a combined set of independent variables. In so doing, it provides weights for each independent variable, which indicates how much of this 'explained' variance can be attributed to each independent variable holding constant the effects of all the other independent variables.

Survey analysis taking account of a third variable, multiple regression and causal path analysis are examples of multivariate analysis. The term is also used for techniques such as factor analysis that seek to simplify description of an array of variables by reducing them to a smaller number of basic factors.

Correlation and causality

What MVA can do is to reveal and elaborate associations between measured variables, which is not the same as identifying causes. A cause involves a constant conjunction between X (or a combination of Xs) and Y, such that whenever X (Xs) occur Y results. In principle this requires a perfect correlation (R=1) between the identified Xs and Y. MVA, of course, is used to indicate causal factors when this condition does not obtain. The crux, then, as to whether MVA reveals causal factors, turns on the notion of 'factor'. If factor is seen as indicative of causal relationship rather than as a cause per se, then MVA can be seen as a means to reveal causal factors.

Thus, if several studies show some association between lack of supervision and delinquency, then supervision may be seen as a causal factor, although not, of itself, a sufficient cause. Unless a perfect correlation between a number of factors and delinquency is found, then the sufficient conditions will remain undisclosed. MVA merely points to possible causal combinations.

This, of course, inhibits any possibility of causal laws, indeed MVA cannot do other than suggest macro-sociological causal factors and cannot attribute causality. Indeed, the technique is purely statistical and any causal inference goes beyond MVA itself. Cause implies a time priority, if X causes Y then X precedes Y. The specification of time priority is independent of the statistical procedures. Similarly, any causal attribution is dependent upon a prior selection of relevant variables, MVA can only indicate the association between specified variables. Causal attribution is thus dependent upon a prior selection of theoretically sound variables.

At one level MVA reveals causal factors in as much as it provides a basis for elaborating non-spurious correlations, which if located within a sound theoretical framework in which time priority can be demonstrated, may suggest causal relationships. However, these are mere suggestions, MVA cannot reveal the existence or nature of any causal links in the sense of proving them or providing the basis of causal laws at a theoretical level. MVA is a pragmatic device that may suggest causal factors, on the basis of a falsificationist principle, assuming that it is viable to talk about macro-sociological causes in the social world.

Measurement

MVA deals with relationships between measured variables. It thus elaborates associations between operationalised concepts. There is a difference between 'revealing causal factors' at this operational level and constructing causal laws at a universal theoretical level.

The extent of association between operationalised concepts may be a function of the operationalising process, which is a multi-stage process involving subjective decisions about the following: the dimensions encompassed by a theoretical concept; the selection of indicators of each dimension; their combination into an index. It has been argued that 'objective' criteria are possible for the construction of an index, and that the 'interchangeability of theoretically sound indicators' obviates the subjectivity of the selection procedure (Lazarsfeld). However, even accepting these caveats, the researcher still makes 'subjective' decisions as to the components of the operationalised concept. MVA, in dealing with measured variables, is thus dealing with these selectively operationalised concepts and can only suggest causal links for these operational constructs. The bridge between theoretical causal attribution and identification of operational causal factors is therefore clearly problematic.

Multivariate analysis and falsificationism

MVA assumes a nomothetic approach to the social world, (i.e. that one may construct the social world on the basis of generalisable cause and effect). Specifically, the orientation towards this positivistic endeavour adopted by multivariate analysis is a falsificationist one. That is, theoretical statements are not proved. Rather they are framed boldly and in a way in which they are open to empirical disproof. Statements that appear corroborated and are not refuted by empirical evidence are, for the time being, accepted as part of scientific knowledge.

MVA adopts this approach in the sense of setting up hypotheses that imply a causal relationship and then openining them up to scrutiny. If a correlation is non-spurious then it is indicative of a causal relationship. The falsificationist approach to the production of scientific production raises problems such as the persistence of clearly refuted statements in science.

The most important objection, however, is that falsificationism does not address the problem of the theory-laden nature of observation. An observed result is interpreted only within the theoretical framework under test. It provides no possibility for the reconceptualising of empirical evidence using an alternative 'paradigm'. MVA revelations, are, then, at best, non-transcendent.

Multivariate analysis using crosstabulations

It is possible to analyse the relationship between two variables taking into account other factors when the data is crosstabulated (i.e. of a nominal or ordinal scale). This is done by constructing n-way crosstabulations (i.e. crosstabulations that are more than simple two way crosstabulations. The approach is to create crosstabulations of X by Y controlling for a third (or any number) of other variables. For a simple example see the entry on spuriousness.

See DARP

analytical review

associated issues

related areas

correlation

falsificationism

operationalisation

regression

Researching the Real World Section 8

Sources