The Use of Structural Equation Modeling in Business

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The Use of Structural Equation Modeling in
Business
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Examples of business research questions

• A 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 with
• MULTIVARIATE 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 Measurement

• The 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 (cant 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 data
• Can 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 business
• Factor 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

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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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WHEN the researcher has any (or all!) of the
following questions?

• Does the original data fit the proposed model?
• Does the data validate a particular theory? Or,
  does the data suggest a different theory?
• How good is my measurement model?
• Do my measured items represent the underlying
  latent construct reliably?
• How good is my structural model?
• Are all the proposed paths significant and in the
  predicted direction?
• Can some paths be removed without hurting the
  model?
• Is mediation present in my model?
• Do different groups (ex small firms vs. large
  firms) need different models? How much better
  is the model for one group over another?

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An Example
Attitude
Subjective Norm
Intention
Perceived Behavioral Control
Behavior
Actual Behavior
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HOW does a researcher perform SEM?

• Draw your proposed model by hand
• Pick 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 program
• Analyze the results

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HOW does a researcher perform SEM?

• Model specification
• Drawing the Path Diagram to represent the
  measurement and structural models
• Identification
• counting parameters and degrees of Freedom
• Estimation of Model
• Evaluation of overall model fit
• Interpretation of the parameter estimates
• Model modifications
• Either those suggested by the computer program or
  suggested by competing theories
• Communicating SEM results

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HOW to draw the proposed model?

• MODEL A statistical statement about
  relationships among variables
• Undirected 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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An Example
Attitude
Subjective Norm
Intention
Perceived Behavioral Control
Behavior
Actual Behavior
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An Example
Attitude
Subjective Norm
Intention
Perceived Behavioral Control
Behavior
Actual Behavior
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HOW to draw the Path Diagram?

• 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

• Relationships between variables are indicated by
  lines
• Straight lines with one arrow direct (causal)
  relationship between two variables
• Curved line with 2 arrows correlational
  relationship between variables

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More Modeling Terms to Know

• Exogenous constructs not caused or predicted
  by any other variables
• Like an independent variable in regression
• No arrows pointing to them
• Endogenous constructs constructs predicted by
  one or more constructs
• Like a dependent variable in regression
• Arrows in the path diagram lead to endogenous
  constructs

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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?
• Minimum1, 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 c2 (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 c2/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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An Example of a nested model
Attitude
Subjective Norm
Intention
Perceived Behavioral Control
Behavior
Actual Behavior
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How do you know your model is right?

• CONFIRMATORY STRATEGY
• Researcher specifies a single model and SEM is
  used to assess its statistical significance
• All or nothing approach confirmation bias
• 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