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The Use of Structural Equation Modeling in Business

Suzanne Altobello Nasco, Ph.D.Assistant Professor of Marketing

Southern Illinois University

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Examples of business research questionsA CEO wants to examine how her company is perceived,

relative to its competitors. She asks respondents to rate the similarity of every possible paired combination of firms to find out which competing firms are similar/dissimilar to her own company.

A company is designing a new type of answering machine and wants to know which attributes are most important to consumers in the new product design. They present several product combinations to a focus group and ask respondents to rank order the product combinations.

A stockbroker has 50 clients. He wants to organize these clients into groups based on the clients’ responses on several variables that measure risk tolerance, income, age, and years until retirement.

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More business research questions The human resource department wants to predict

whether a person should be hired or not, based on all available information from their job application.

A firm is examining the effectiveness of its advertising and wants to know whether the type of publication (magazine vs. television show) and the nature of the publication (entertainment vs. news) affect attitudes towards the ad, the brand, and the company.

An academic department wants to determine which variables (such as age, grade average and IQ) can differentiate between successful, moderately successful, and not successful students.WHAT DO THESE EXAMPLES HAVE IN COMMON?

They all can be answered withMULTIVARIATE STATISTICS

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Multivariate Statistics - Defined All statistical methods that simultaneously analyze

multiple (more than 2) measurements on each individual or object under investigation.

Multivariate statistics are an extension of univariate and bivariate statistics. Univariate = analyses of single variable distributions Bivariate = analyses of two variables where neither

is an Independent Variable or Dependent Variable Multivariate = analyses of multiple I.V.s and D.V.s,

all correlated with one another to varying degrees. In other words, their different effects cannot

meaningfully be interpreted separately.

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Basic Concepts in Multivariate Statistics The “VARIATE” = The building block of all

multivariate statistical analyses A linear combination of variables with

empirically determined weights

Variate = w1 X1 + w2 X2 + …. + wn Xn The variables (Xs) are specified by the researcher,

the weights (ws) are determined by the multivariate technique to meet a specific objective.

The result is a single value representing a combination of the entire set of variables that best achieves the goal of the specific multivariate test.

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Important Decision: Variable MeasurementThe first consideration when choosing the

appropriate multivariate method of analysis is how the researcher measured the variables.

Two types of data: Non-metric / Qualitative: Categorical, DISCRETE

values. If you are in one category, you can not be in the other (can’t

be both male and female).

Metric / Quantitative: Measured on a scale that changes values smoothly/continuously.

Variables can take on any value within the range of the scale and the size of the number reflects the “amount”, “quantity”, “degree” or “magnitude” of the variable.

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Determining the appropriate Multivariate Technique to use

Must ask 3 questions of the dataCan the variables be divided into independent

and dependent variables (based on theory)?How many variables are dependent?How are the independent and dependent

variables measured (metric or non-metric)? Answering these 3 questions will lead you to the

appropriate multivariate technique to perform However, these questions WILL NOT relate the

multivariate technique to your original questions or hypotheses of interest.

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Examples of Interdependent Multivariate Techniques

In interdependent techniques, there are no “independent” or “dependent” variables Instead, the researcher is looking for some

structure in the data OR wants to reduce the number of variables in the analysis

3 primary interdependent techniques in businessFactor analysis (reduce survey questions into

fewer factors)Cluster analysis (group respondents or objects)Multidimensional Scaling (identify competitors)

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Examples of Dependent Multivariate Techniques

Variables divided into independent and dependent One Metric DV, ≥ 2 metric IVs

Regression One Non-Metric DV (2 levels), ≥ 2 metric IVs

Logistic Regression One Non-Metric DV (2 or more levels), ≥ 2 metric IVs

Discriminant Analysis One metric DV, ≥ 1 categorical IV(s)

Analysis of Variance (ANOVA) More than one metric DVs, ≥ 1 categorical IV(s)

Multivariate Analysis of Variance (MANOVA)

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Introducing Structural Equation Modeling

WHAT is SEM?

WHY should a business researcher use this tool?

WHEN does a researcher use SEM?

HOW does the researcher perform this analysis?

HOW is an SEM analysis interpreted?

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WHAT is Structural Equation Modeling?

Structural Equation Modeling (SEM) is “a comprehensive statistical approach to testing hypotheses about relations among observed and latent variables” (Hoyle, 1995)

SEM is an extension of several multivariate techniques Multiple regression, Factor analysis, Canonical

Correlation, MANOVA, Mediational analysis

Also called: simultaneous equation modelinganalysis of covariance structures

confirmatory factor analysis

causal modelingcausal analysispath analysis

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WHY should business researchers use SEM? SEM can be used to test existing theories or

help to develop new theories SEM can examine several dependent

relationships simultaneously. Other bivariate & multivariate techniques can only

examine one dependent variable at a time. SEM can test relationships between one or more

IVs (either continuous or discrete) and one or more DVs (either continuous or discrete).

Both IVs and DVs can be either previously-detected factors (via factor analysis) or can be measured variables (e.g., items on a survey).

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WHEN should a researcher use SEM?

When the researcher wants to estimate multiple and interrelated dependence relationships And has “a priori” theory

When the researcher wants to represent unobserved (unmeasured or latent) concepts in these relationships

When the researcher wants to account for any measurement error in the estimation process And has “multiple measures” for each latent

construct

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An Example

Attitude

PerceivedBehavioral

Control

SubjectiveNorm

Intention

ATT 1

ATT 2

ATT 3

PBC 1

PBC 2

PBC 3

SN 1

SN 2

INT 1

INT 2

INT 3

Behavior Actual Behavior

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HOW does a researcher perform SEM?

Draw your proposed model by handPick a statistical package (LISREL, EQS, AMOS)

Use the raw data or input a correlation / covariance matrix of all of your MEASURED (manifest) variables

Within the program, draw your model precisely OR write lines of programming code that represent relationships in your model

Run the model via the computer programAnalyze the results

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HOW to draw the proposed model?MODEL = A statistical statement about

relationships among variablesUndirected relationships: correlational Directed relationships: causal

TWO parts of every SEM model: “Structural Model” The underlying pattern of

dependent relationships (among unobservable constructs)

“Measurement Model” The specific rules of correspondence between manifest and latent variables

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HOW to draw the “Path Diagram”?

Relationships between variables are indicated by linesStraight lines with one arrow: direct (causal)

relationship between two variablesCurved line with 2 arrows: correlational relationship

between variables

• Measured variables: manifest variables or indicators that are represented by squares or rectangles

● Latent variables: constructs, factors, or unobserved variables that are represented by circles or ovals

Factor 1

v1 Typically described as an item on a questionnaire;Denoted with all lowercase letters

u1

Unique unobserved variable; typically used to represent measurement disturbance/error unique to the manifest variable it is affecting

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HOW to design an SEM study? Sample Size: SEM is a “large-sample technique”

Consider “number of subjects per estimated parameter” (10 subjects per parameter)

Usually want at least 200 subjects How many indicators (variables) should be used

to represent each construct? Minimum=1, but 3 is the preferred minimum

(allows for empirical estimation of reliability) with an upper limit of 5-7

Can use Correlation matrix OR Covariance matrix (among all measured variables) as input

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HOW to evaluate SEM output? Chi Square: 2 (want value to be non-significant)

For models with about 75 to 200 cases, this is a reasonable measure of fit.  But for models with more cases, the chi square is almost always significant. 

Normed Chi Square: 2/df (want between 1 and 2-3) Root Mean Square Error of Approximation

(RMSEA) (want .05 or less) Takes an average of the residuals between the

observed and estimated matrices Many “_FI” measures (want greater than .90)

GFI, AGFI, CFI, Normed Fit Index (NFI), NNFI We want convergence on multiple fit

indices to claim our model is “good”

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How do you know your model is “right”?

1. CONFIRMATORY STRATEGY• Researcher specifies a single model and

SEM is used to assess its statistical significance

• All or nothing approach; confirmation bias

2. COMPETING MODELS STRATEGY• Nested model: same number of

constructs and indicators but number of estimated relationships (parameters) changes.

• Not all competing models are nested!!

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HOW to make model modifications? Comparing alternate models

Compare the 2 of “null” model with your current model (we WANT the difference to be significant, meaning your model is significantly better than null)

Can also look at the 2 difference in “nested” models For non-nested models, compare AIC values (from EQS)

Examining individual paths for model changes Use Lagrange Multiplier Test (LM) to see if model will

improve with the addition of more parameters & use Wald Test (W) to determine if the model will improve if you remove a parameter

Model modifications must be made judiciously, with respect to your original theory and the goal of SEM (theory-testing, exploration, confirmation)

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HOW to use SEM to build theory? SEM is the only multivariate technique that is

(almost) completely theory-driven If your Fit Indices are all good, your parameter

estimates match your predictions, your structural model fits as predicted AND your measurement model is good, then you can say you have strong support for your model…..HOWEVER,

There is no single “correct” model; no model is unique in the level of fit achieved For any model with an acceptable “fit”, there are a

number of alternative models with the same level of model fit!

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Several Important SEM Articles Kenny, David A. and Deborah A. Kashy (1992). Analysis of the

Multitrait-Multimethod Matrix by Confirmatory Factor Analysis. Psychological Bulletin, 112(1), 165-172.

Bagozzi, Richard P. and Youjae Yi (1989). On the Use of Structural Equation Models in Experimental Designs. Journal of Marketing Research, 26 (August), 271-284.

Bagozzi, Richard P. (1978). Salesforce Performance and Satisfaction as a Function of Individual Difference, Interpersonal, and Situational Factors. Journal of Marketing Research, 15 (November), 517-531.

Fornell, Claes and David F. Larcker (1981). Evaluating Structural Equation Models with Unobservable Variables and Measurment Error. Journal of Marketing Research, 18 (February), 39-50.

MacCullum, Robert C. and James T. Austin (2000). Applications of Structural Equation Modeling in Psychological Research. Annual Review of Psychology, 51, 201-226.

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Several good SEM websites http://www.gsu.edu/~mkteer/semfaq.html  Ed Rigdon's (Department

of Marketing, Georgia State University) SEM Frequently Asked Questions

http://users.rcn.com/dakenny/causalm.htm  Dave Kenny's (Department of Psychology, University of Connecticut) SEM tutorial site

http://www.utexas.edu/cc/stat/software/lisrel/  Good introduction (manuals, tutorials) of LISREL program, maintained by University of Texas at Austin.

http://www.ssicentral.com/lisrel/mainlis.htm  Excellent LISREL site with tutorials, maintained by SSI Scientific Software International.

http://www.mvsoft.com/  Homepage for EQS software