doing quantitative research 26e02900 6 ects cr n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Doing Quantitative Research 26E02900, 6 ECTS Cr. PowerPoint Presentation
Download Presentation
Doing Quantitative Research 26E02900, 6 ECTS Cr.

Loading in 2 Seconds...

play fullscreen
1 / 57

Doing Quantitative Research 26E02900, 6 ECTS Cr. - PowerPoint PPT Presentation


  • 82 Views
  • Uploaded on

Doing Quantitative Research 26E02900, 6 ECTS Cr. Olli-Pekka Kauppila Daria Volchek. Lecture IV - May 21, 2014. Today’s lecture. AM session Structural equation modeling PM session Multilevel research design. Learning objectives – AM session.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Doing Quantitative Research 26E02900, 6 ECTS Cr.' - lily


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
doing quantitative research 26e02900 6 ects cr

Doing Quantitative Research26E02900, 6 ECTS Cr.

Olli-Pekka Kauppila

Daria Volchek

Lecture IV - May 21, 2014

today s lecture
Today’slecture

AM session

  • Structural equation modeling

PM session

  • Multilevel research design
learning objectives am session
Learning objectives – AM session

Get familiar with the basic idea of structural equation modeling

Identify special characteristics of SEM

Develop understanding of the latent variable constructs

Understand the process of SEM

Develop skills to interpret the quality of models and research results obtained with the application of SEM

research question
Researchquestion

Organizational

commitment

Role

ambiguity

Emotional

exhaustion

Job

satisfaction

Intention

to leave

Role

conflict

Performance

Babakus, E., Cravens, D. W., Johnston, M., & Moncrief, W. C. (1999). The Role of Emotional Exhaustion in Sales Force Attitude and Behavior Relationships. Journal of the Academy of Marketing Science, 27(1), 58-70.

Whatare the antecedents and consequences of the emotionalexhaustion of the individualswhodo ”peoplework”?

how many regression analyses do you need to estimate this model
How many regression analysesdoyouneed to estimatethismodel?

Organizational

commitment

Role

ambiguity

Emotional

exhaustion

Job

satisfaction

Intention

to leave

Role

conflict

Performance

Babakus, E., Cravens, D. W., Johnston, M., & Moncrief, W. C. (1999). The Role of Emotional Exhaustion in Sales Force Attitude and Behavior Relationships. Journal of the Academy of Marketing Science, 27(1), 58-70.

generalization of regression
Generalization of regression

SEM is like regression:Y = B0 + B1X1 + B2X2 + e

With assumptions intact, regression is beautiful, but . . .

SEM, a generalization, helps us address some of regression’s limitations

what is sem
What is SEM?

amultivariatestatisticaltechnique

whichcombines (confirmatory) factoranalysis and multipleregression modeling

  • Cansimultaneouslytestmeasures and structuralrelationships

for the purpose of analyzinghypothesizedrelationships

  • Testsmodelsthatareconceptuallyderived, a priori
  • Testsif the theoryfits the data

amonglatent (i.e. unobservedortheoretical) variablesmeasuredbymanifestvariables (i.e. observedorempiricalindicators)

what is sem1
What is SEM?

SEMencompasses an entirefamily of modelsknownbymanynames, e.g. covariancestructureanalysis, latentvariableanalysis, confirmatoryfactoranalysis, LISRELanalysis

  • LInearStructiralRELationships
  • TechnicallyLISREL is a computerprogramdevelopedby Karl Jöreskog and Dan Sörbom to docovariancestructureanalysis
  • Alsoothersoftwaresareavailable for SEM: AMOS, Mplus…
what is sem2
What is SEM?

SEMtypicallyconsists of twoparts (orsub-models):

The measurementmodel

  • specifieshowlatentvariablesdependuponorareindicatedby the observedvariables
  • describesthe measurementproperties (reliabilities and validities) of the observedvariables

The structuralequationmodel

  • specifiescausalrelationshipsamong the latentvariables
  • describes the causaleffects
  • assigns the explained and unexplainedvariance
why sem
WhySEM?

Organizational

commitment

Managerial

support

Intention

to leave

Job

satisfaction

Environmental

perceptions

The keybenefits of SEMare:

  • Estimation of multiple and interrelateddependencerelationships via series of separate, butinterdependent, multiple regression equations

SEMallows to accomodatecontinuous, dummy, and categoricalmeasures.

why sem1
WhySEM?

The keybenefits of SEMare:

  • Estimation of multiple and interrelateddependencerelationships via series of separate, butinterdependent, multiple regression equations
  • Ability to modelbothobserved and unobserved (latent) variables and account for measurementerror in the estimationprocess (parameterestimatescloser to populationvalues)
why sem2
WhySEM?

The keybenefits of SEMare:

  • Estimation of multiple and interrelateddependencerelationships via series of separate, butinterdependent, multiple regression equations
  • Ability to modelbothobserved and unobserved (latent) variables and account for measurementerror in the estimationprocess (parameterestimatescloser to populationvalues)
  • Ability to define a model to explain the entire set of relationshipssimultaneously
what is a latent variable
What is a LatentVariable?
  • A latentvariableis an unobservedconceptthatcanonlybeapproximatedbyorservableormeasurablevariables(i.e. happiness, satisfaction, emotionalexhaustion), oftencalledfactor.
  • The observedvariables, whicharegatheredfromrespondentsthroughvarious data collectionmethods, areknown as indicatorsormanifestvariables.
latent variables as presumed cause of item values reflective measure
Latentvariables as presumedcause of itemvalues (reflectivemeasure)

Observed

variable

Observed

variable

Latent

variable

Factor

Manifestvariables/

indicators

Observed

variable

The latentvariable is viewed as an underlyingconstructthatgivesrise to somethingthat is observed(i.e. an observedvariable).

latent variables as summary of the measurements formative measure
Latentvariables as summary of the measurements (formativemeasure)

Observed

variable

Observed

variable

Latent

variable

Factor

Manifestvariables/

indicators

Observed

variable

The latentvariable is viewed as a summary (weights of the relativeimportance) of the observedvariables. Changes in the indicatorscausechange in the latentvariable.

classroom exercise i
Classroomexercise I

In yourresearchprojectyouareinterested in identifying the antecedents and consequences of firm international performance

Based on yourextensiveliteraturereview, youhavefound out thatbothreflective and formativemeasurescouldbeused for firmperformance

Thus, youdecide to operationalizeboth:

  • Comeup with measureitemsthatyouthinkwouldcapturefirm international performance (1) in a reflective and (2) in formative manner
firm international performance
Firm international performance
  • Formative:
  • Percent of foreignsales in totalsales;
  • N of countries a firmhasentered;
  • Percent of foreignclients a firmhas.

Reflective:

Generally speaking, we are satisfied with our success in international markets;

We have achieved the turnover objectives we set for internationalization;

We have achieved the market-share objectives we set for internationalization;

Internationalization has had a positive effect on our company’s profitability;

Internationalization has had a positive effect on our company’s image;

Internationalization has had a positive effect on the development of our company’sexpertise;

The investments we have made in internationalization have paid off.

measurement error
Measurementerror

No matter how concrete we think our variables are, they always contain some error when we try to measure them.

Measurement error is that proportion of the variable which our measure is unable to capture for variousreasons (systematicorrandom).

It is vital to consider the amount of error in our measurement, no matter how confident we are that we have’gotitright’.

However, in all other multivariate techniques we assume there isno error in variables.

measurement error1
Measurementerror

The impact of measurementerror:

βyx = βs* ρx

βyx – observed regression coefficient

βs – truestructuralcoeffients

ρx – reliability of the predictorvariable

Unless the reliability is 100%, the observedcorrelation (and resulting regression coefficient) willalwaysunderstate the ”true” relationship.

sem correction for measurement error
SEMcorrection for measurementerror

SEM ”accounts for” or ”corrects for” the amount of measurementerror in the variables (latentconstructs) and estimateswhat the relationshipwouldbeiftherewas no measurementerror.

βs= βyx / ρx

Dueto thiscorrection, SEM regression coefficientsaremoreaccurate (closer to populationvalue) and tend to belargerthancoefficientsobtained with multiple regression analysis.

incorporating errors
Incorporatingerrors

Delta – an errortermassociated with an estimated, measured

x-variable

x1

δ1

x2

δ2

Role

ambiguity

x3

δ3

x4

δ4

x5

δ5

types of relationships in a sem model
Types of relationships in a SEMmodel

δ1

x1

δ1

x1

Role

ambiguity

δ2

x2

Role

ambiguity

δ2

x2

δ3

x3

δ3

x3

Emotional

exhaustion

δ4

x4

δ4

x4

Role

conflict

y3

y2

y1

δ5

x5

Role

conflict

x5

δ5

δ6

x6

δ6

x6

ε1

ε2

ε3

(1) Correlation (2) Dependence

types of variables in sem model
Types of variables in SEMmodel

y6

y5

y4

Exogenousvariables

Endogenousvariables

x1

Organizational

commitment

Role

ambiguity

x2

x3

Intention

to leave

Emotional

exhaustion

Job

satisfaction

x4

y12

y11

y9

y8

y10

y3

y7

y2

y1

Role

conflict

x5

x6

Notexplainedbyanyotherconstruct in the model

Determinedbyconstructswithin the model

importance of theory
Importance of theory

SEMmodelshouldnotbedevelopedwithoutunderlyingtheory!

SEManalysesshouldbedictatedfirst and foremostby a strongtheoreticalbase.

Theoryimpliesconsequences, some of whicharetested vs. data. Refutinganyconsequencesrefutes the theory (i.e. SEM is primarily a confirmatorymethod)

testing theory based models
Testingtheory-basedmodels

Modelimplies a pattern in the covariancematrix

Undermultiple regression assumptionsintact, wecancomparemodel-impliedcovariancematrix with empiricalcovariancematrix (i.e. the onebased on the collected data)

If the difference in covariancematrices is nonsignificant, weconfirm the hypothesizedtheoreticalrelationships (χ2 test)

theory driven modeling strategy
Theory-drivenmodelingstrategy

Confirmatorymodelingstrategy – the researcherspecifies a single modelcomposed of a set of the relationships and usesSEM to assesshowwellitfits the data (iteitherworksoritdoesn’t)

Competingmodelsstrategy – estimatedmodel is compared with alternativemodels (e.g. a test of competingtheories)

  • Equivalentmodels– modelshave the samenumber of parameters with differentrelationshipsbetweenthem, and the alternativemodel(s) fits at least as well as the proposedmodel

Modeldevelopmentstrategy– althoughbasicframework is proposed, a purpose of modeling is to improvethisframeworkthroughSEMmodeifications

causation evidence in sem
Causationevidence in SEM

Covariation – SEMcandeterminesignificantcovariationbetween the cause and effectconstructs;

Sequence – causation in the temporalsequancecouldbeprovidedthroughexperimentalorlongitudinalresearch design;

Nonspuriouscovariation – the size and nature of the relationshipbetween the cause and the effectshouldnotbeaffectedbyincludingotherconstructs (variables) in the model (Support=>Job satisfaction and Work environment)

Theoreticalsupport – compellingtheoreticalrationale to support a cause-and-effectrelationship

input matrix covariance matrix
Input matrix: Covariancematrix

SEMdiffers from other multivariate techniques in that it uses only the variance-covariance or correlation matrix as its input data.

Individual observations can be input into the programs, but they are converted into one of these two types of matrices before estimation.

The focus of SEM is on the pattern of relationships acrossrespondents.

number of observed indicators
Number of observedindicators

How many indicators should be used per construct?

The minimum number of indicators for a construct is one

− but the use of only a single indicator requires the researcher to provide estimates of reliability

A construct can be represented with two indicators, but three is the preferred minimum number of indicators

− because using only two indicators increases the chances of reaching an infeasible solution

There is no upper limit in terms of the number of indicators.

− In practice, 5-7 indicators should represent most constructs

what is cfa
What is CFA?

Confirmatory factor analysis – tests the extend to which a researcher’sa-priori, theoreticalpattern of factorloadings on prespecifiedconstructsrepresents the actual data (i.e. confirmsorrejectsourpreconceivedtheory)

The factorsareassignedbased on the researcher’spriortheoreticalknowledge (statisticaltechniquedoesnotassignvariables to factorslike in ExploratoryFactor Analysis)

Eachmeasuredvariableloadsonly on onepre-definedfactor

Cross-loadingsarenotassigned

CFA providesinformationabout the validities and reliabilities of the observedindicators

stages in cfa
Stages in CFA

1. Developing a theoretically based model

2. Constructing a path diagram of causal relationships

3. Converting the path diagram into a set of measurement model

4. Choosing the input matrix type

5. Assessing the identification

6. Evaluatinggoodness-of-fitcriteria

7. Interpreting and modifying the model (if theoretically justified)

assumptions of path diagram
Assumptions of pathdiagram

First, all causal relationships are indicated.

Theory is the basis for inclusion or omission of any relationship.

It is just as important to justify why a causal relationshipdoes not exist between two constructs as it is to justify the existence of another relationship.

Yet it is important to remember that the objective is to model the relationships among constructs with the smallest number of causal paths or correlations among constructs that can be theoretically justified (parsimonious).

assumptions of path diagram1
Assumptions of pathdiagram

Second, all causal relationships are assumed to be linear.

Nonlinear relationships cannot be directly estimated in structural equation modeling, but modified structural models can approximate nonlinear relationships.

Assumption of linearity of the relationships requires all other assumptions for multivariate analysis to hold true

example of measurement cfa model
Example of measurement (CFA) model

Role

ambiguity

Role

conflict

Intention

to leave

Emotional

exhaustion

Job

satisfaction

y9

y8

y6

y5

y7

y3

y4

y2

y1

x3

x6

x2

x5

x1

x4

ε1

ε2

ε3

ε4

ε5

ε6

ε7

ε9

ε8

δ5

δ1

δ2

δ3

δ4

δ6

  • x1-x3correlate, butcorrelation is zeroifweidentify a common cause of x1-x3, i.e. ”Roleambiguity”
  • Indicatorsareunidimensional, errortermsshouldnotbecorrelated
  • First, wetest the measures (wecanfixit)
  • Second, wetest the theorybetween the constructs
translating the picture into simplis
Translating the picture into SIMPLIS

Role

ambiguity

Role

conflict

Intention

to leave

Emotional

exhaustion

Job

satisfaction

y9

y8

y6

y5

y7

y3

y4

y2

y1

x3

x6

x2

x5

x1

x4

ε1

ε2

ε3

ε4

ε5

ε6

ε7

ε9

ε8

δ5

δ1

δ2

δ3

δ4

δ6

ROLCONF1 = 1*Rolconf

ROLCONF2= Rolconf

ROLCONF3 = Rolconf

EMEXH1 = 1*Emexh

EMEXH2= Emexh

EMEXH3= Emexh

JOBSAT1 = 1*Jobsat

JOBSAT2= Jobsat

JOBSAT3= Jobsat

LEAV1 = 1*Leav

LEAV2= Leav

LEAV3= Leav

e.g. Rolam = W1(ROLAM1) + W2(ROLAM2) + W3(ROLAM3)

ROLAM1 = 1*Rolam

ROLAM2 = Rolam

ROLAM3 = Rolam

how does cfa look like
How does CFA look like?

Errorterm

Observed

variable

Factorloading

Latent

construct

Correlation

between

latentconstructs

evaluating goodness of fit criteria assessment of measurement model
Evaluatinggoodness-of-fitcriteria(assessment of measurementmodel)

In evaluating the measurement part of the model, focus on the relationships between the latent variables and theirindicators (i.e. manifestvariables).

The evaluation of the measurement part of the model should precede the detailed evaluation of the structural partof the model.

The aim is to determine the validity and reliability of the measures used to represent the constructs of interest.

− validity reflects the extent to which an indicator actually measures what it is supposed to measure

− reliability refers to the consistency of measurement (i.e. the extent to which an indicator is free of random error)

evaluating goodness of fit criteria loadings
Evaluatinggoodness-of-fitcriteria:Loadings

The next step is to examine the estimated loadings and to assess the statistical significance of each one.

- critical t-values:

when α=.01, criticalt-value=2.33

when α=.05, criticalt-value=1.645

when α=.10, criticalt-value=1.282

If statistical significance is not achieved, the researcher may wish to eliminate the indicator or attempt to transform it for better fit with the construct.

evaluating goodness of fit criteria loadings1
Evaluatinggoodness-of-fitcriteria:Loadings

One problem with relying on unstandardizedloadingsand associatedt-values is thatitmaybedifficult to compare the validity of differentindicatorsmeasuring a particularconstruct.

  • Indicators of the sameconstructmaybemeasures in verydifferentscales, ifthis is the case, thendirectcomparisons of the magnitudes of the loadingsareclearlyinappropriate
  • It is recommendedthat the magnitudes of the standardizedloadingsarealsoinspected (completelystandardizedsolution)
evaluating goodness of fit criteria r 2
Evaluatinggoodness-of-fitcriteria:R2

Reliability of the indicatorscanbeexaminedbylooking at the squaredmultiplecorrelations (R2) of the indicators

  • they show the proportion of variance in an indicatorthat is explainedbyitsunderlyinglatentvariable
  • the rest is due to measurementerror
  • highmultiplesquaredcorrelationsvaluedenoteshighreliability for the indicator
evaluating goodness of fit criteria composite reliability cr
Evaluatinggoodness-of-fitcriteria: Compositereliability (CR)

In addition to assessing the reliability of the individualindicators, it is possible to calculate a compositereliabilityvalue for eachlatentvariable

  • alsoknown as constructreliability
  • to dothisuseinformation on the indicatorloadings and errorvariancesfrom the CompletelyStandardizedSolution
  • with single itemmeasures, it is notpossible to empiricallyestimate the reliability (couldbefixed at 1.0=noerrororestimatedby the researcher)
composite reliability cr
Compositereliability (CR)

Recommendedthresholdvalue is .60

The reliabilityfor the latentconstructmustbecomputedseparately for eachmultipleindicatorconstruct in the model.

LISRELdoesnotcomputethemdirectlybutprovidesallnecessaryinformation.

average variance extracted ave
Averagevarianceextracted (AVE)

Anothermeasure of reliability is the varianceextractedmeasure

Reflects the overallamount of variance in the indicatorsaccounted for by the latentconstruct

Highervarianceextractedoccurwhen the indicatorsaretrulyrepresentative of the latentconstruct

The AVEmeasure is a complementarymeasure to the CRvalue

average variance extracted ave1
Averagevarianceextracted (AVE)

AVE is quitesimilar to the CRmeasurebutdiffers in that the standardizedloadingsaresquaredbeforesummingthem

Guidelinesuggestthat the varianceextractedvalueshouldexceed .50 for a construct

classroom exercise ii
Classroomexercise II

Calculate the reliabilitymeasures (CR and AVE) for the twolatentvariablesbelow:

classroom exercise ii1
Classroomexercise II

Calculate the reliabilitymeasures (CR and AVE) for the twolatentvariablesbelow:

Latentvariable 1:

  • CR = 0.770602 => exceeds the common threshold of 0.60
  • AVE = 0.403557 => lower than 0.50

Latentvariable 2:

  • CR = 0.744912 => exceeds the common threshold of 0.60
  • AVE = 0.423463 => lower than 0.50
evaluating goodness of fit criteria
Evaluatinggoodness-of-fitcriteria

Next step is to assess overall model fit with one or more goodness-of-fitmeasures

Goodness-of-fit measures reflect correspondence of the actual or observed input (covariance or correlation) matrix with that predicted from the proposed model.

There are three types of Goodness-of-fit measures:

  • Absolute fit measures
  • Incremental fit measures
  • Parsimonious fit measures
evaluating goodness of fit criteria1
Evaluatinggoodness-of-fitcriteria

Absoluteindices:

  • Chi-square:provides a test of perfectfit in which the nullhypothesis is that the modelfits the population data perfectly (i.e. wewant the chi-squaretest to benon-significant p>.05)
  • RMSEA (RootMean Square Error of Approximation)

Focuses on the discrepancybetween a predicted and observedcovariance per degree of freedom

Takes into account the modelcomplexity

Showshowwellwould the model, with unknownbutoptimallychosenparametervalues, fit the populationcovariancematrixifitwasavailable

Ideallybelow 0.05

evaluating goodness of fit criteria2
Evaluatinggoodness-of-fitcriteria

Incrementalindices:

  • NormedFit Index (NFI)
  • Non-normedFit Index (NNFI)
  • ComparativeFit Index (CFI)
  • Goodness of Fit Index (GFI)

Parsimonyindices:

  • Adjustedgoodness of Fit Index (AGFI)
  • Allideallyabove 0.90
from measurement to structural model
Frommeasurement to structuralmodel

ε4

ε5

ε6

y6

y5

y4

ζ2

δ1

x1

Organizational

commitment

Role

ambiguity

δ2

x2

ζ4

ζ1

ζ3

δ3

x3

Intention

to leave

Emotional

exhaustion

Job

satisfaction

δ4

x4

y12

y11

y9

y8

y10

y3

y7

y2

y1

Role

conflict

x5

δ5

δ6

x6

ε7

ε8

ε9

ε11

ε12

ε1

ε2

ε3

ε10

δn – measurementerror in exogenous (independent) variables

εn– measurementerrorin endogenous (dependent) variables

ζn – covariationbetween the endogenousvariableserrors

testing the hypotheses
Testing the hypotheses

y6

y5

y4

x1

Organizational

commitment

-.223*

-.164*

Role

ambiguity

x2

.514*

.495*

x3

Intention

to leave

Emotional

exhaustion

Job

satisfaction

-.322*

-.252 *

x4

y12

y11

y9

y8

y10

y3

y7

y2

y1

Role

conflict

x5

.392*

x6

fit indices for structural model
Fitindices for structuralmodel

Sameindices as for a measurementmodelapply:

  • Chi-square, p-value
  • RMSEA
  • Allotherincrementalindices (NFI, NNFI, CFA, GFI)
  • Parsimonyindices (AGFI)
let s sum up
Let’ssumup

SEM…

Providesintegrativefunction

Helpsresearchers to bemoreprecise in theirspecification of hypotheses and operationalization of constructs

Takes into accountreliability of measures in tests of hypotheses in waysgoingbeyond the averaging of multi-itemmeasures of constructs

Guidesconfirmatoryresearch in a manner of combiningself-insight with theory

Oftensuggestsnovelhypothesesoriginallynotconsidered and opensup new avenues for research

Is useful in experimental and surveyresearch, cross-sectional and longitudinalstudies, measurementorhypothesistesting, withinoracrossgroupsand institutionalorculturalcontexts

Is easy to use

Is fun