Appendix Related user acceptance models

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Appendix PMX CTM function sets

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9

2

Appendix Related user acceptance models

Only a fraction of the available user acceptance models are mentioned in this thesis. This appendix gives a short overview of the other models that are available.

DETERMINANTS OF THE PERCEIVED EASE OF USE

The parsimony of TAM strength is it strength but also has a major limitation. It is predictive but its generality does not provide sufficient understanding from the standpoint of providing system designers with the information necessary to create user acceptance for new systems. As it provides understanding little is known about the determinants of EOU.

To get a better understanding of the EOU it can be split up into several determinants.

THE MOTIVATIONAL MODEL

A significant body of research in psychology has supported a general motivation theory as an

explanation of behavior. Davis applied this motivational theory to understand new technology adoption and use. From the perception that users will want to perform an activity:

♦ Extrinsic motivation; “because it is perceived to be instrumental in achieving valued outcomes that are distinct from the activity itself such as improved job performance, pay, or promotions”.

♦ Intrinsic motivation; “for no apparent reinforcement other than process of performing the activity per se”

THE MODEL OF PC UTILIZATION

Derived largely from Triandis (1977) theory of human behavior, this model presents a competing perspective to that proposed by TRA and TPB. Thompson et al. (1991) adapted and refined Triandis’

model for IS contexts and used the model to predict PC utilization.

Core constructs; job-fit, complexity, long-term consequences, affect toward use, social factors, facilitating conditions.

THE INNOVATION DIFFUSION THEORY

Grounded in sociology, IDT (Rogers 1995) has been used since 1960s to study variety of innovations, ranging from agricultural tools to organizational innovation. Within information systems, Moore and Benbasat (1991) adapted the characteristics of innovations presented in Rogers and refined a set of constructs that could be used to study individual technology acceptance.

Core constructs; relative advantage, ease of use, image, visibility, compatibility, results demonstrability, volunatriness of use.

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10 THE SOCIAL COGNITIVE THEORY (SCT)

One of the most powerful theories of human behavior is social cognitive theory (Bandura 1996).

Compeau and Higgins (1995) applied and extended SCT to the context of computer utilization. The model studied computer usage but the nature and the model and the underlying theory allow it to be extended to acceptance and use of information technology in general.

Core constructs; outcome expectations from performance, outcome expectations from persona, self- efficacy, affect, anxiety

TAME

Jackons, Chow and Leich developed a model that incorporated user involvement (participation in the system development process by potential users or their representatives) and other psychological constructs.

If more social research is submitted, for example media usefulness, a further investigation of other social factors is needed. Karahanna and Straub added the items social presence and social influence to Davis technology acceptance model.

TASK CHANGE

Although the system offers important benefits for the organization as a whole, sometimes the organization could not overcome the resistance of individuals that do not perceive the benefits as important to the individual jobs.

Intrinsic motivation is viewed as a function of the nature of the task performed. As such, it can be distinguished from extrinsic motivation, arising from the system of incentives presented to the task performed, which can often be manipulated without changing the data itself.

Although many specific characteristics that lead to intrinsic motivation were identified in the management literature, most fall into one (or more) of three categories: control, over task activities, job, and organization are generally proposed to be motivating, arousal, Stems from the individual’s desire to achieve or maintain a particular mental state, and achievement, The individual’s own perception of performance, e.g. quality, competence or performance.

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USER SATISFACTION

There are several scales that can be used for estimation user satisfaction. Some of the most popular scales are those of Bailey and Pearson (1983), Baroudi and Orlikowski (1988), Ives, Olsen and Baroudi (1983) and Jenkins and Ricketts (1985).

Rogers (1995) estimates fives stages (Figure B1), every stage estimates systems acceptance among users.

Figure B1 innovation diffusion process

Knowledge Æ Persuasion Æ Decision Æ Implementation Æ Confirmation

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Appendix Beliefs structures and Decomposition

A

TTITUDINAL BELIEF STRUCTURES

There are three salient characteristics of an innovation that influence adoption (Rogers, 83):

Relative advantage

The degree to which an innovation provides benefits which supersede those of its precursor and may incorporate factors such as economic benefits, image enhancement, convenience and satisfaction. This should be positively related tot Attitude.

Complexity

The degree to which an innovation is perceived to be difficult to understand, learn of operate. Generally, the simpler an innovation is to understand and use, the more likely it is to be adopted. Thus, complexity is expected to relate negatively to Attitude.

Compatibility

The degree of how an innovation fits with the potential adopter’s existing values, previous experiences and current needs. Compatibility will relate positively related to adoption.

N

ORMATIVE BELIEFS STRUCTURE

Normative information from others has two consequences (factors) (Insko and Cialdini (69)).

Confidence and self-esteem effects

As one’s self-confidence rises relative to confidence in others, belief change and yielding decline (Jaccard, 81) . Thus persons with high self-esteem probably have less need for social approval and should exhibit less conformity (Robinson and Shaver, 73).

Familiarity effects

When consumers are uncertain about the proper level of affect, the perceptions of significant others will be used to solidify an attitude (Strenthal and Craig, 82). Alternatively on the basis of a familiarity and learning experiment, “experienced consumers use their knowledge of the product class to limit their research” (Johnson and Russo, 84).

Innovativeness effects

Innovators’ adoption decisions are “essentially independent of the interpersonal communications network” (Midgley and Dowling, 78). Next to that sometimes in innovation process some persuading is necessary, example is that an influence can occur of the ones with the most convincing opinion.

Involvement effects

One generally finds that increased involvement reduces persuasion effects (Sherif and Sherif’s, 67). On the other hand enduring importance (involvement) is positively related to search, information sensitivity, and word-of-mouth (Bloch and Richins, 83). Thus, it is unknown how involvement may affect crossover path. One might speculate that countervailing effect may prevail and that the net effect will not be different from that observed in the sample as a whole.

Age and Gender effects

The extent that elderly persons perceive themselves as competent, susceptibility to social influence is not heightened (Philips and Sternthal, 77). However, when personal perceive them as competent, susceptibility to social influence is not heightened. The gender literature also suggests that due to traditional social roles women tend to be slightly more persuadable than men (Cooper, 79).

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C

OGNITIVE BELIEF STRUCTURE

There are three attribute subsets that can be identified; Inconveniences, Encumbrances, and Rewards.

R

ELATED ISSUES

Socratic effect (Petty and Cacioppo, 81)

Belief structures become more logically consistent as a result of having been stated publicly. Others perceive consistency in their thoughts.

False consensus (Shimap and Kavas, 84)

Exists when persons believe that their own behavior is common and appropriate and, therefore, that a high consensus must exist for their own belief structure.

Research on this phenomenon suggests that two variables may moderate the degree to which it is manifest in any given situation.

Self-esteem

A study showed that “depressed” subjects showed less false consensus than did non-depressed subjects.

Causal focus

Individuals who view live outcomes, as current determined will perceive others as subject to similar life interpretations and desires. Alternatively, individuals who make personal attributions should view themselves independently of the feelings of others.

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4

Appendix Questionnaire

Algemeen deel

Eerst wat algemene vragen over je achtergrond.

Wat is je naam? ………

Ben je een key-user van het PMX systeem? Ja/nee

Wat is het percentage dat je per training hebt bijgewoond?

EDB ……..

PALETTI ……..

DISY ……..

WRAP-UP ………

Hoeveel uren heb je zelfstandig (dus toen er geen cursus was) het systeem getest? ……….

Ben je van het vrouwelijk of mannelijk geslacht? Vrouwelijk/mannelijk

In welke leeftijdcategorie zit je? - 25 - 33

- 33 – 40 - 40 – 47 - 47 – 55 - 55 – 63

Wat is je functie in de organisatie? ………..

Hoeveel jaren werkervaring heb je? ………

Hoeveel jaren werkervaring heb je op CTM gebied? ……….

Intentiemodel

Dit zijn vragen om het theoretisch model te testen.

In hoeverre ben je het met de volgende stellingen eens? Waarbij –3 aangeeft dat je het er helemaal niet mee eens bent en + 3 aangeeft dat je het er helemaal wel mee eens bent.

Ik heb geen problemen met de kwaliteit van de output van PMX.

Helemaal niet mee eens -3 -2 -1 0 1 2 3 helemaal mee eens

Het gebruik van het systeem vind ik plezierig.

Gezien de middelen, kansen en de kennis die nodig zijn om het systeem te gebruiken zal het makkelijk voor mij zijn om het systeem te gebruiken.

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14 Helemaal niet mee eens -3 -2 -1 0 1 2 3 helemaal mee eens

Ik denk dat ik liever het PMX systeem gebruik dan S-ware om de status van een studie te kunnen bekijken.

Het zal eenvoudig voor mij zijn om handig in de omgang met PMX te worden.

De technische kennis van ProPack Data vind ik uitstekend.

Mensen die in mijn werkomgeving invloed (collega’s) op mijn gedrag hebben denken dat ik het systeem moet gebruiken.

Het is mij niet duidelijk hoe ik het systeem moet gaan testen.

Ik heb de benodigde kennis om het systeem te gebruiken.

Mensen waarvan ik de mening respecteer denken dat ik het systeem niet moet gebruiken.

Door het gebruik van PMX kan ik mijn werk makkelijker doen.

Wanneer ik tegen problemen aanloop tijdens het testen vind ik dat snel genoeg om hulp kan vragen.

Ik zie niet gelijk hoe ik het resultaat/de output kan gebruiken voor mijn werk.

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De organisatie vindt dat ik het systeem moet gebruiken

Ik vind dat het PMX systeem een toename is van kwaliteit op het CTM gebied.

Ik loop vaak tegen dingen aan die onbekend zijn voor organisatie waar ik nieuwe creatieve oplossingen voor moet bedenken.

Ik heb duidelijk kunnen aangeven wat voor inbreng ik wil geven aan de pilot voor PMX.

Ik vind dat ik op vrijwillige basis mee doe aan de pilot voor PMX.

Ik vind PMX eenvoudig te gebruiken.

Ik vind het makkelijk om de gewenste informatie te vinden in het PMX systeem.

Ik heb controle over het gebruik van het systeem.

De zaken die ik tegenkom in mijn werk hebben vaak raakvlakken met verschillende bedrijfsgebieden.

Het systeem komt niet overeen met systemen die ik al gebruik.

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16 Mijn intentie is om het PMX systeem te gebruiken i.p.v. S-ware.

Tijdens mijn werk kom ik veel verschillende groepen mensen tegen waar ik mee om moet gaan.

Ik heb niet de juiste middelen die nodig zijn voor het systeem.

Ik denk dat het afwegen van producten makkelijker gaat.

Op alle facetten vind ik het PMX systeem betrouwbaarder in gebruik dan de huidige systemen.

Ik vind dat ik genoeg tijd heb gestoken in het testen en trainen van PMX tot nu toe.

Het hebben van het systeem is een status symbool van de organisatie

Het gebruik van PMX zorgt voor een productiviteitsverbetering.

Ik vind dat ik genoeg vragen aan ProPack Data kan stellen.

Het leren kennen van PMX zal eenvoudig voor mij zijn.

Het gebruik van het systeem is een goed idee.

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Ik zie het gebruik van PMX als een toegevoegde waarde voor mijn taken.

Ik vind het idee niet prettig dat ik straks het systeem moet gaan gebruiken.

Tijdens mijn werk heb ik vaak te maken met plotselinge problemen waar ik oplossingen voor moet zoeken.

De aankoop van het systeem maakt PDD een strategisch betere partner.

Ik denk dat ik liever Disy gebruik om dingen af te wegen dan de huidige weegmethodes.

Het gebruik van PMX zal zorgen voor een kwaliteitsverbetering van het CTM proces.

De output van het PMX systeem vind ik vergelijkbaar met die van het huidige systeem.

Ik denk dat ik precies weet hoe ik moet oefenen met het systeem zodat ik het optimaal kan gebruiken.

Het gebruik van PMX zorgt voor een verbetering van de efficiency van het CTM proces.

Mensen in de organisatie die functioneel meer aanzien hebben dan ik maken gebruik van het systeem.

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Ik denk dat ik Paletti vaker ga gebruiken dan het huidige systeem om magazijninformatie te vinden.

Mensen die belangrijk voor mij zijn denken dat ik het systeem moet gebruiken.

Het is mij duidelijk hoe het resultaat gebruikt kan worden.

Ik vind PMX nuttig in het CTM proces.

Ik vind het niet eenvoudig om PMX te laten doen wat ik wil.

Voor mijn werk is het gebruik van het systeem relevant.

De omgeving waarin het testen plaats vindt, vind ik zeer aangenaam.

Het gebruik van het systeem is een slim idee.

Ik vind het resultaat niet direct toepasbaar.

PMX zorgt ervoor dat ik mijn taken sneller kan doen.

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19 Ik vind dat de kwaliteit van de output van PMX hoog is.

Het belang van de aankoop van het systeem zit voornamelijk bij het hoger management.

Graag zou ik willen zien dat er in de planning ruimte wordt vrijgemaakt zodat ik met het systeem kan oefenen.

Mijn supervisor vindt dat ik het systeem moet gebruiken.

De interactie met het systeem is eenvoudig voor mij.

Ik vind dat ik weinig ervaring heb met systemen die overeenkomstig zijn met PMX.

Voor mijn werk is het gebruik van het systeem van belang.

Ik vind dat het systeem op een makkelijker manier dingen kan structuren.

Ik vind dat ik goed zelfstandig kan werken met de computer

Ik hoef niet aan te geven hoeveel inzet ik wil geven aan de pilot voor PMX.

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20 Computervaardigheden

Onderstaand zijn een aantal capaciteiten genoemd die betrekking hebben op computervaardigheden in het algemeen. Hierbij is het van belang dat je een onderscheid maakt tussen het systeem PMX waar de vorige vragen over gingen en deze vragen die over je computervaardigheden in het algemeen gaan.

Geef per variabele aan in hoeverre je dit beheerst. Dit gebeurt op basis van een schaal van 1 tot 7, waarbij de1 staat voor heel slecht en de 7 staat voor heel goed.

1. Het kunnen begrijpen en interpreteren van Output.

Input van een systeem zijn alle zaken die jij als gebruiker aan het systeem toevoegt. Dit kunnen gegevens zijn maar ook variabelen en instellingen. Alles wat eruit komt en wat het systeem dus op levert is de output. Output is dus het gehele resultaat van het systeem. Hierbij kan gedacht worden aan gegevens die worden gepresenteerd nadat bepaalde berekeningen zijn verricht maar ook zaken die op je beeldscherm verschijnen en die worden geprint.

Heel slecht 1 2 3 4 5 6 7 Heel goed

2. Het kunnen vinden van de benodigde Data.

Data zijn alle gegevens die je wil bereiken via de computer. Dit zijn gegevens op je eigen harde schijf, op het netwerk of die zich ergens op het Internet bevinden.

3. Het kunnen gebruiken van Hardware.

Hardware zijn de elektronische computeronderdelen. Voorbeelden hiervan zijn het toetsenbord, de kaarten in een computer maar ook de aangehechte weegschaal.

4. Het kunnen Programmeren.

Betreft de vaardigheid om computerprogramma’s te kunnen maken.

5. Het kunnen gebruiken van Operating systems.

Dit zijn systemen die gebruikt worden om alle processen op een computer te kunnen reguleren. Het meeste bekende en gebruikte systeem hiervan is Windows.

6. Het kunnen gebruiken van Application software

Deze software betreft alle applicaties die speciaal ontworpen zijn voor bepaalde toepassingen. Hierbij moet je voornamelijk denken aan systemen die gemaakt worden voor bepaalde doeleinden, zoals bijvoorbeeld SAP. Echter er zijn ook andere voorbeelden zoals TRIM en FlowChart.

7. Het kunnen gebruiken van Software development tools.

Dit is software dat gebruikt wordt om andere software te maken. Hier maak je gebruik van verschillende programmeertalen. Te denken valt hierbij aan Oracle.

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21 8. Het gebruik van Office automation software .

Hierbij gaat het om verschillende soorten software die gebruikt worden ter ondersteuning van het kantoorwerk. Zoals het bijhouden van het gebruik van alle mogelijkheden van Outlook (mail, agenda, adresboek, mailinglijsten etc.) en andere toepassingen van Microsoft Office (zoals Word, Excel etc.).

Daarnaast ook Fax management, omgaan met digitale plaatjes, virus en anti-spam software etc.

9. Het kunnen toepassen van Beeldtechnieken.

Dit betreft het kunnen bewerken van plaatjes en video’s op de computer.

10. Het maken van Modellen.

Deze vaardigheid betreft het omzetten van ideeën en interpretaties in bepaalde schema’s en voorbeelden op de computer. Hierbij kan je denken aan bijvoorbeeld het maken van flowcharts.

11. Het kunnen omgaan met Datacommunicatiesystemen.

Hier gaat het om netwerk toepassingen zoals het kunnen aanleggen van een netwerkverbinding, instellingen voor Internet en het kunnen installeren van een server.

Tevens wil ik vragen of jullie bovenstaande items willen waarderen op mate van belangrijkheid voor het optimaal kunnen gebruiken van het PMX systeem.

Dit zal ik verder toelichten. Je kan je voorstellen dat sommige van de bovengenoemde vaardigheden van belang zijn om met het PMX systeem te werken zoals bijvoorbeeld het begrijpen en interpreteren van Output en het kunnen gebruiken Applicatie Software. Tevens zijn er ook vaardigheden die in mindere mate van belang zijn voor het optimaal gebruik van PMX. Je kan dan denken aan het kunnen Programmeren of het kunnen omgaan met Software development tools.

De vraag is nu aan jou of je alle bovenstaande 11 vaardigheden in een bepaalde prioriteit kan zetten waarbij, in jouw ogen, de belangrijkste vaardigheden die nodig zijn voor PMX bovenaan staan en degene die het minst belangrijk zijn onderaan.

Meest belangrijk

Prioriteit Itemnummer Vaardigheid 1

2 3 4 5 6

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22 7

8 9 10 11 Minst belangrijk

Ruimte voor extra opmerkingen.

………..

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5

Appendix Structural Equation Modelling

Causal modeling

Different analyzing methods in science are based on latent variables. These are several hypothetical constructs that are related to each other in several ways. Generally there exists no operational method for directly measuring these constructs. A mathematical model is proposed to explain the properties of the measured variables in terms of the hypothesized latent variables. The primary statistical problem is one of optimizing the parameters of the model and determining the goodness-of-fit model.

The analyzing methods can be categorized as exploratory or confirmatory in nature. More traditional factor analyses are data exploration methods, these have the purpose to generate hypothesis. Herewith factors are needed to explain the relationship among observed indicators and confirm when a preexisting model of the relationship among the indicators directs the search. More modern methods are related to the confirmatory methods. Here factor analysis is not concerned with a discovering a factor structure, but with confirming the existence of a specific factor structure.

Techniques for Structural Equation Modeling

Structural equation modeling is a second-generation data analyses technique. In contrary to regression analysis, one of the first generation, SEM enables a researcher a single, systematic and comprehensive analysis.

The holistic analysis that SEM is capable of performing is carried out via one of the two distinct statistical techniques.

1. Covariance analysis (LISREL, EQS and Amos) 2. Partial Least Squares (PLS)

The objective of PLS is, overall, the same as that of linear regression. To show high R² and significant t- values, thus rejecting the null hypothesis of no-effect. The objective of the covariance is, however, to show that the null hypotheses are insignificant. Another important difference is the degree to which items load only on their respective constructs without having “parallel correctional patterns” [Segars, 1997]. Furthermore an advantage of the covariance based SEM is that it can compare alternative pre- specified measurement models.

Some researchers thus suggest that PLS is more suited for predictive applications and theory building.

It should be used as a complementary technique to covariance based analysis. PLS estimates the parameters in such a way the residual variance are minimized of all the dependent variables, consequently PLS is less affected by small sample sizes.

Different steps in SEM methodology can be specified [Bollen and Long, 1993].

1 Specification – Statement of the theoretical model in terms of equations or a diagram.

2 Identification – The model can in theory be estimated with observed data.

3 Estimation – The model’s parameters are statistically estimated form data.

4 Model fit – The estimated model parameters are used to predict the correlations or co-variances between measured variables and the predicted correlations or co-variances are compared to the observed correlations or co-variances.

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24 Structural models

A structural equation model contains two inter-related models, the measurement model and the structural model. The principle of this kind of causal modeling is the linear regression equation.

This specifies the hypothesized effects of certain variables (predictors) on another variable. A path diagram is given and equations (and/or matrices) are extracted. Arrows indicate causal of directional influences and the strength of each effect is indicated by the weight of each arrow.

Exogenous latent variables are synonymous with independent variables; they ‘cause’ fluctuations in the values of other latent variables in the model. Changes in the values of exogenous variables are not explained by the model, there are influenced by other factors external to the model. Endogenous latent variables are synonymous with dependent variables and as such, are influenced by the exogenous variables in the model, either directly of indirectly.

Models can only be tested if the models parameters of the model can be uniquely specified or identified. A useful causal model must be over identified; it must have fewer parameters than data points.

Path diagrams are graphical representations of these a prior specified structures, and, if appropriate assumptions are met, ordinary least squares (OLS) estimates of regression coefficients can be used to estimate the strengths of the structural relationships specified in the diagram.

For any two variables, three basic relationships are possible, a structural

influence, a mutual structural influence and no structural relation but the constructs might covary.

A path diagram represents a set of structural equations, that is, a set of univariate regression equations with specified structure among the variables in the model.

The representation is in the form of a general path analytical model:

Y = α + ΒY + ΓX + ζ x = Λxξ + δ

y = Λyη + ε

Abbreviations used for structural equation modeling x = q x 1 vector of observed exogenous variables y = p X 1 vector of observed endogenous variables ξ = n x 1 vector of latent exogenous variables η = m x 1 vector of latent endogenous variables δ = q x 1 vector of measurement errors in x ε = p x 1 vector of measurement errors in y

Λx = q x n regression matrix that relates n exogenous factors to each of the q observed variables to designed to measure them.

Λy = p x m regression matrix that relates m exogenous factors to each of the p observed variables to designed to measure them.

Γ = m x n matrix of coefficients relating n exogenous factors to the m endogenous factors В = m x m matrix of coefficients relating m endogenous factors to one another

ζ = m x 1 vector of error residual representing errors in the equation relating η and ξNY the number of endogenous variables Y

Ψ (psi) m x m symmetrical variance-covariance matrix among the m residual errors for the m endogenous factors

Θε (theta-epsilon) symmetrical p x p variance-covariance matrix among the errors of measurement for the p endogenous observed variables.

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25 Statistic in SEM

The biggest disadvantage of using covariance models is the danger that it does not converge. When the model gives a warning about a non-positive or adds a ridge to the covariance matrix. Covariance based SEM generate statistics about three levels:

At the individual path and construct level

At the model fit level Individual path modification indexes.

Item loadings and measurement error (with t-values)

Likelihood-ratio chi-square (χ²). A insignificant (good model) is with a p-value above .05 or just as small as possible.

Easy to add a path that may significantly improve model fit.

Constrcut reliability (Cronbach’s α,

> .70)

Ratio chi-square and degrees of freedom must be between 1 and 3.

Coefficients and t-values of latent constructs.

Goodness of fit (GFI) measures the absolute fit (not adjusted) of the combined measurement and structural model.

Squared Multiple Correlation (SMC), the explained variance of each latent construct.

Adjusteed GFI (AGFI) adjust this value with the degrees of freedom.

Standardized Root Mean Residual (RMR) assesses the residual variance of the observed variables and how these correlate among each other.

Normed Fix Index, the normed difference in χ² between a zero factor null model with no common variance across measures and a proposed multi-factor model.

Although there is a universal agreement among researchers that the larger the sample the more stable the parameter estimates, a cautious attempt a rule of thumb suggest that the sample size should always be more than 10 times the number of free model parameters. Otherwise, the results from the asymptotically distribution free (ADF)/weighted least squares (WLS) method should not be trusted.

Another alternative to deal with non-normal data is to make the data more normal looking by introducing some normalizing transformations on the raw data; power transformations (e.g. square

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26 each data point), square root transformations, reciprocal transformations, and logarithmic transformations.

The most used program is LISREL (LInear Structural RELations modeling). A major shortcoming is that it has difficulties using small sample sizes. For estimation different statistical techniques can be used. All statistical techniques are discussed in appendix X, where the maximum likelihood technique is the most commonly used. Parts of LISREL are the PRELIS and SIMPLIS programs.

PRELIS suits as a preprocessor for LISREL where it can be used to analyze raw data that is intended for further analyses. An example is its ability to make a covariance or correlation matrix.

SIMPLIS is added in a newer version of the program. With using the SIMPLIS method the complexity of the program is reduced and the use of LISREL is easier for beginners in the field of SEM analyses.

Using the ML method will yield a chi-square (_χ²) value to evaluate the goodness-of-fit of the model. The chi-square is compared to the degrees of freedom. The problem with the chi-square value is that it is very sensitive to sample size. Only moderate samples are applicable.

The sensitivity has influence on the nonconvergence (NC) of the model. Related to this are; the use of small samples which has an effect on the standard errors, the size of the factor loadings and how many indicators are used per factor (NI/NF ratio). In general it can be addressed that increased information, in the form of independent observations, generates more reliable measurements.

Other methods are the generalized least squares (GLS) or the weighted least squares method.

Mathematical formulas

Β and Γ determine the structure of the particular path model. In addition, a (NX * NX) variance/covariance matrix, Φ of exogenous variables and a (NY * NY) variance/covariance matrix, Ψ of elements in ζ can be specified.

Together these four basic matrixes completely determine a particular path model.

0 0 0 γ¹¹σ²ζ1 0 0

Β = β²¹ 0 0 Γ = γ²¹ Φ = σ^2X1 Ψ = 0 σ²ζ2 0

β³¹β³²0 γ³¹0 0 σ²ζ3

Variance

∑Nk=1 (Xk - µ^X)²

N

Covariance

∑Nk=1 (Xk - µ^X) (Yk - µ^X) N

Correlation

Covariance matrix of Y

Σ

Σyyyy(Θ(Θ)) == EE((yyyy’’)) == (I(I –– BB))-1-1((ΓΓΦΦΓΓ’’ ++ Ψ)Ψ) ((II –– B

B))--11’’ σ^X2 =

σ^XY =

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9 Covariance matrix of X

Σ

Σxxxx(Θ(Θ)) == EE((xxxx’’)) == ΦΦ

Covariance matrix of XY Σ

Σxxyy((ΘΘ)) = = EE((xxyy’’)) =Φ=ΦΓΓ’’((II –– B)B)^-^-1¹

Some assumptions that are made:

- the exogenous and endogenous variables are measured with no or negligible error and have a mean of 0 [E(X) = E(Y) = 0]

- The structural relations form exogenous to the endogenous observed variables are linear.

The error terms in ζ have a mean of 0 [E(ζ) = 0] and are independent and uncorrelated.

Goodness-of-fit tests

In general there are at least three results for the difference between the observed covariance matrix S and the reproduced covariance matrix ∑.

1. If the difference is small, it can be concluded that, it represents the observed data reasonably well.

2. The proposed model may be deficient, in the sense that it is not capable of emulating the analyzed matrix even with most parameter values.

3. The data may not be good.

Equivalent models may imply very different conceptualizations of the data, and are thus differentiable at the theoretical level; but at the statistical level, there is a problem of indeterminacy in the selection of a ‘true’ model.

SEM involves three primary constructs:

• Indicators (observed variables). These are usually represented as squares. For questionnaire- based research each indicator represents a particular question.

• Latent variables (or constructs, concept, factors). Represent a phenomena that cannot be measured directly.

Path relationships (correlation, one- or two-way paths). Relate to hypotheses that state the relations among the latent variables.

The problem of the goodness of fit is how to decide whether, the population covariance matrix, is sufficiently similar to, sample matrix. To objective is to conclude that a model adequately fits a particular data. The mostly applied chi-square goodness-of-fit index has several limitations regarding sample size.

STAND-ALONE INDEXES

Maximum likelihood fitting function (FF) & the scaled likelihood ratio (LHR)

The FF and LHR are the basis for the χ² test statistic and most other fit indexes. When there is a perfect fit, FF while have the value of 0.0 and LHR takes a 1.0 value.

χ²and χ²/df ratio

The chi-square ratio is mostly applied when these ratios will vary with sample size.

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9 Root-mean-square residual (RMR)

The square root of the mean of the squared residuals in S and E. RMR must be interpreted in relation to the size of the variances and covariances of the measured variables and cannot be compared across applications based on different variables.

Goodness-of-fit Index (GFI) and adjusted GFI (AGFI)

GFI is a measure of the relative amount of variances and covariances jointly accounted by the model.

There is no dependence on sample size. If applying AGFI mean squares are used instead of total sums of squares.

Information criterion

Cudeck and Browne proposed an index that is useful for comparing different indexes of fit. Different variations can be made for this index.

Critical N

To estimate the sample size that is critical to make an adequate fit.

NESTED MODELS

Several researchers in structural equation modeling showed that even with small sizes valid information could be obtained. By comparing the results of multiple, nested, models.

A null model with all the variables to be uncorrelated is compared with a target model. If the fit of the null model is reasonable, then the fit of a target model will automatically be reasonable. If, however, the fit of the null model is unreasonable, then there is little covariance to explain and no basis of support for the target model even if it also fits the data.

Two indexes are proposed that are useful of comparing the fit of a particular model across samples that have unequal sizes. One of the two alternative forms of the 10 stand-alone indexes can be used to derive incremental indexes.

To apply this method, five nested models are used:

1. a null model (Mn) that contains no paths among the constructs 2. a saturated model(Ms) that links all constructs

3. a theoretical model (Mt) representing the theoretical model to be tested 4. a constrained model (Mc) that constrains theoretically defensible paths in Mt.

5. a unconstrained model (Mu)that frees theoretically defensible paths in Mt

Cheng proposes a second nested approach. This is empirically different as the measurement and the structural model is revised so that the model with most appropriate fit is proposed. This is showed in the understanding figure.

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10 Tucker-Lewis Index (TLI)

An example of the second type index, also referred to as the nonnormed index. The TLI is based on the χ²/df ratio.

The Bentler-Bonett index (BBI)

Based on the χ^2,for the null model the chi-square should be larger than for the target model.

Parismony index

Invokes a penalty function for using additional parameters by multiplying a Type 1 incremental index by function of the df/s for the null and target models.

Marsh, Balla and McDonald conducted empirical research with several seven sample sizes and four different data sets among the three types of indexes (stand-alone, type 1 and type 2). This has proven that when using smaller sample sizes Type 2 incremental indexes are most appropriate; FFI2, LHRI2, χ^2/I2, TLI and CAKI2.

The disadvantage of the normed index is that the values of the measures tend to increase with sample size. This comparison across samples with different Ns is risky and that assessments of fit in small samples may be overly pessimistic and that assessments of fit in small samples may be overly pessimistic.

Rather than choosing between a normed measure whose means are related to N and a nonnormed one whose means are no, I believe that the best strategy is to report both types of measures to give a more complete evaluation.

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11 The statistic T reflects the closeness of the null model, to the sample matrix S, the sample covariance matrix in covariance structure analysis, in the chi-square metric. Acceptance or rejection of the null hypothesis via a test based on T may be inappropriate or incomplete in model evaluation for several reasons.

1. Some basic assumptions underlying T may be false and the distribution of the statistic may not be robust to violation of these assumptions.

2. No specific model Σ(θ) may exist in the population, and T is intended to provide a summary regarding closeness of Σ (dakje) to S, but not necessarily a test of Σ (dakje) = Σ(θ(dakje).

3. In small samples T may not be chi-square distributed.

4. In large samples, any a prior hypothesis may be rejected.

5.

Boomsma (1982) suggest that whenever wanting to reduce the risk of drawing erroneous conclusions LISREL test should not use samples of less than 200.

Bentler and Bonnett normalized incremental fit index as an additional means of assessing the overall fit of a causal model. They approach the true value and their variances become very small as sample size increases. Samples larger than, an incremental fit index below .95 indicates that the model does not adequately fit the data even for very simple models. For larger sample, over 500, this measure should be close to one.

Data-Model fit

The a priori hypothesized model is tested whether or not the data fits the model. An overview will be given that indicates some of the overall measures of fit.

Chi-square statistic

The test evaluates whether or not the unrestricted population variance/covariance matrix of the observed variables ∑ is equal to the model-implied variance covariance matrix ∑(0), i.e. it tests whether or not the hypothesis H0: ∑ = ∑(0).

Goodness-of-Fit (GFI)

By using Jöreskog and Sörbom’s (1981) indexes is to determine the amount of observed variance/covariance information that can be accounted for by the hypothesized model. An index gives an indication between 0 and 1, where closer to one indicates a better fit.

F [S, ∑(θ)]

F [S, ∑(0)]

Where the numerator value of the fitting function F for the hypothesize model, while the denominator is the minimum value of F when no model is hypothesized.

Validity & Realibility

The validity of an instrument simply refers to the measure’s overall property of indeed measuring what it was designed to measure. Traditionally a diversification can be made between three different kinds of validity,

- Content-related validity indicate how well items or scales cover the intended content. Two types of can be generated statistically: internal consistency and the correlation of scales with other measures of the construct.

GFI = 1 -

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12 - Criterion-related validity is determined by computing a correlation coefficient (validity

coefficient), between the instrument and a standard. However the errors of the standard or not corrected. Application can be to measure the difference between the self-reported and observed behavior. Types that can be distinguished are

o In predictive validity, the operationalization's ability to predict something it should theoretically be able to predict is assessed.

o In concurrent validity, the operationalization's ability to distinguish between groups that theoretically can be distinguished are assesed.

- Construct-related validity the instrument constructs are tested. A high correlation between the measurements associated constructs is wanted. Next to that a low correlation between different constructs are assessed. Exploratory factor analysis can sometimes be used to include related latent constructs in validity of a certain construct.

o In convergent validity, similarity between operational functionality of the instrument with related instruments are examined.

o In discriminant validity, differences between operationalization of the model and theoretical different models. Differences in chi-squares can be used to consider these differences.

An instrument’s reliability refers to how constituently the instrument measures whatever it was designed to measure.

- test-retest reliability determines stability of the measurements over time and is estimated when two test of the same constructs are submitted at different periods in time.

- parallel forms reliability a measure of the equivalence of two forms of the same test.

Due to the time lag between measurements, a disadvantage of both approaches is the potential presence of carry-over effects (practice, memory, attitude) that might lead to either an under- or overestimation of the reliability of a measure.

- A single test is necessary with an internal consistency check. Calculating the correlations between two parts of the test is the most straight forward way. Alternative approaches are the computing the two halves using the Kuder-Richardson formulas (KR-20 or KR– 21) or the Cronbach alpha coefficient.

1 ( 1) Nxr N xr

α

=

+ −

If the inter-item correlation is low, alpha will be low. If the inter-item correlations are high, then there is evidence that the items are measuring the same underlying construct. Then a “good” or

“high” reliability could be stated. However Cronbach alpha is based on the assumption that all underlying items are equally important.

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13

6

Appendix Quantitative Data

Correlation Matrixes of Independent Variables

BI TTF TF TE TC --- --- --- --- --- BI 1.00

TTF 0.74 1.00

TF 0.82 1.10 1.00

TE -0.10 0.28 0.34 1.00

TC 0.44 0.27 0.37 - - 1.00

W_A_R_N_I_N_G: Matrix above is not positive definite

Global Goodness of Fit Statistics, Missing Data Case

-2ln(L) for the saturated model = 0.000 -2ln(L) for the fitted model = 5854.075

Degrees of Freedom = 291

Full Information ML Chi-Square = 5854.07 (P = 0.0) Root Mean Square Error of Approximation (RMSEA) = 0.44

Time used: 13.399 Seconds

Age

Sample size normal Old = 4

Middle = 5 Young = 5

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14 Transformed 120

Old Two-stage least squares

Correlation Matrix of Independent Variables

BI U A EOU SE SN --- --- --- --- --- ---

BI 1.00

U 0.84 1.00

A 0.33 -0.53 1.00

EOU 1.13 0.88 0.12 1.00

SE 1.18 1.04 -0.14 1.14 1.00

SN 0.01 0.73 -1.28 0.18 0.42 1.00

PBC 0.92 0.82 -0.34 0.89 1.07 0.50

PBC --- PBC 1.00

MIddle

BI U A EOU SE SN --- --- --- --- --- ---

BI 1.00

U 0.92 1.00

A 0.77 0.84 1.00

EOU 0.91 1.01 0.80 1.00

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15 SE 0.98 0.98 0.89 0.90 1.00

SN -0.34 -0.51 -0.33 -0.48 -0.62 1.00

PBC 0.77 0.91 0.77 0.91 0.80 -0.29

PBC --- PBC 1.00

Young

BI U A EOU SE SN --- --- --- --- --- ---

BI 1.00

U 1.06 1.00

A 0.97 0.85 1.00

EOU 0.46 0.49 0.35 1.00

SE 0.18 0.30 -0.26 0.26 1.00

SN 0.54 0.37 0.47 -0.47 -0.10 1.00

PBC 0.58 0.45 0.59 0.82 -0.07 0.10

PBC --- PBC 1.00

Men

BI U A EOU SE SN --- --- --- --- --- ---

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16 BI 1.00

U 0.73 1.00

A 0.29 0.67 1.00

EOU 0.23 0.57 0.58 1.00

SE 0.32 0.47 0.45 0.63 1.00

SN 0.13 0.18 -0.07 -0.72 -0.44 1.00

PBC 0.45 0.73 0.66 0.86 0.61 -0.28

PBC --- PBC 1.00

Women

BI U A EOU SE SN --- --- --- --- --- ---

BI 1.00

U 0.99 1.00

A 0.84 0.85 1.00

EOU 0.99 1.01 0.83 1.00

SE 0.83 0.83 0.72 0.75 1.00

SN -0.66 -0.75 -0.63 -0.67 -0.75 1.00

PBC 0.89 0.93 0.75 0.97 0.60 -0.61

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17 Correlation Matrix of Independent Variables

PBC --- PBC 1.00

TAM

A BI EOU U --- --- --- --- A 1.00

BI 0.92 1.00 (0.05)

16.98

EOU 0.82 0.74 1.00 (0.06) (0.05)

14.29 13.72

U 1.08 1.05 0.85 1.00 (0.04) (0.02) (0.03)

27.29 50.76 24.62

Goodness of Fit Statistics

Minimum Fit Function Chi-Square = 4591.01 (P = 0.0)

Normal Theory Weighted Least Squares Chi-Square = 1484.94 (P = 0.0) Estimated Non-centrality Parameter (NCP) = 1320.94

90 Percent Confidence Interval for NCP = (1201.40 ; 1447.92)

Minimum Fit Function Value = 41.36

Population Discrepancy Function Value (F0) = 11.90

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18 90 Percent Confidence Interval for F0 = (10.82 ; 13.04)

Root Mean Square Error of Approximation (RMSEA) = 0.27 90 Percent Confidence Interval for RMSEA = (0.26 ; 0.28) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.00

Expected Cross-Validation Index (ECVI) = 14.21 90 Percent Confidence Interval for ECVI = (13.13 ; 15.35) ECVI for Saturated Model = 3.78

ECVI for Independence Model = 54.90

Chi-Square for Independence Model with 190 Degrees of Freedom = 6054.30 Independence AIC = 6094.30

Model AIC = 1576.94 Saturated AIC = 420.00 Independence CAIC = 6168.67 Model CAIC = 1748.00 Saturated CAIC = 1200.88

Normed Fit Index (NFI) = 0.24 Non-Normed Fit Index (NNFI) = 0.13 Parsimony Normed Fit Index (PNFI) = 0.21 Comparative Fit Index (CFI) = 0.25 Incremental Fit Index (IFI) = 0.25 Relative Fit Index (RFI) = 0.12

Critical N (CN) = 6.05

Root Mean Square Residual (RMR) = 0.29 Standardized RMR = 0.14

Goodness of Fit Index (GFI) = 0.43 Adjusted Goodness of Fit Index (AGFI) = 0.27 Parsimony Goodness of Fit Index (PGFI) = 0.33

BI EOU U --- --- --- BI 1.00

EOU 0.74 1.00 (0.05)

13.66

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19 U 1.06 0.88 1.00

(0.02) (0.03) 51.87 28.16

Population Discrepancy Function Value (F0) = 7.66 90 Percent Confidence Interval for F0 = (6.81 ; 8.59) Root Mean Square Error of Approximation (RMSEA) = 0.28 90 Percent Confidence Interval for RMSEA = (0.26 ; 0.29) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.00

TRA

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20 Model does not converge

A BI SN --- --- --- A 1.00

BI 1.00 1.00 (0.07)

14.33

SN -2.94 -1.58 1.00 (0.07) (0.05)

-39.26 -31.75

Population Discrepancy Function Value (F0) = 5.66 90 Percent Confidence Interval for F0 = (4.93 ; 6.46) Root Mean Square Error of Approximation (RMSEA) = 0.28 90 Percent Confidence Interval for RMSEA = (0.26 ; 0.30) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.00

Model AIC = 763.95

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21 Saturated AIC = 210.00

Independence CAIC = 2196.39 Model CAIC = 879.22

FC SE --- --- FC 1.00

SE 0.83 1.00 (0.06)

15.05

Population Discrepancy Function Value (F0) = 1.15 90 Percent Confidence Interval for F0 = (0.84 ; 1.53) Root Mean Square Error of Approximation (RMSEA) = 0.25 90 Percent Confidence Interval for RMSEA = (0.21 ; 0.28)

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22 P-Value for Test of Close Fit (RMSEA < 0.05) = 0.00

The Modification Indices Suggest to Add the

Path to from Decrease in Chi-Square New Estimate FC4 SE 23.1 2.02

SE1 FC 8.5 -2.27 SE2 FC 9.6 1.09

The Modification Indices Suggest to Add an Error Covariance Between and Decrease in Chi-Square New Estimate FC3 FC1 23.3 1.06

SE1 FC4 12.8 0.78 SE2 FC2 31.7 0.78 SE2 FC3 11.5 0.25 SE3 FC2 9.7 -0.52 SE4 FC2 12.6 -0.41

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23 SE4 FC4 10.4 0.64

SE4 SE2 44.1 -1.16

Tra

TWO-STAGE LEAST SQUARES

Initial Estimates (TSLS)

LAMBDA-X

A FI PH(1 --- --- --- A1 - - - - - - A2 - - - - - - A3 1.45 - - - - A4 0.07 - - - - BI1 - - 1.53 - - BI2 - - - - 1.71 BI3 - - - - 0.55 BI4 - - - - 0.99 BI5 - - - - -0.10 SN1 - - - - - - SN2 - - - - - - SN3 - - - - - - SN4 - - - - - - SN5 - - - - - -

PHI

A FI PH(1 --- --- --- A 1.00

FI -0.21 1.00

PH(1 -0.18 0.64 1.00

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24 THETA-DELTA

A1 A2 A3 A4 BI1 BI2 --- --- --- --- --- ---

2.12 2.39 0.00 1.69 0.00 -0.11

THETA-DELTA

BI3 BI4 BI5 SN1 SN2 SN3 --- --- --- --- --- ---

2.56 0.71 1.93 2.08 0.82 3.14

THETA-DELTA

SN4 SN5 --- --- 2.68 3.98

TAM2

Method of Estimation: Maximum Likelihood

BI EOU I RD OQ JR --- --- --- --- --- ---

BI 1.00

EOU 0.60 1.00 (0.03)

21.22

I 1.20 0.29 1.00 (0.08) (0.08)

15.18 3.70

RD 0.38 0.57 1.58 1.00 (0.03) (0.03) (0.06)

11.83 17.77 26.49

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25 OQ 0.88 0.37 2.02 0.83 1.00

(0.03) (0.04) (0.07) (0.03) 30.64 8.89 27.05 31.02

JR 0.55 -0.14 1.04 0.03 0.55 1.00 (0.02) (0.03) (0.06) (0.03) (0.03)

22.68 -4.78 17.52 0.87 17.73

SN 0.31 -0.55 -0.12 -0.43 -0.32 0.47 (0.06) (0.06) (0.10) (0.06) (0.07) (0.05) 5.06 -9.19 -1.16 -7.26 -4.25 9.04

U 1.00 0.77 1.56 0.66 0.81 0.35 (0.01) (0.02) (0.07) (0.03) (0.03) (0.03) 85.85 36.55 20.84 24.46 26.68 11.79

V 0.24 0.21 1.33 0.39 0.38 0.06 (0.03) (0.03) (0.06) (0.03) (0.03) (0.02) 7.38 6.95 22.23 14.20 12.27 2.56

SN U V --- --- --- SN 1.00

U 0.05 1.00 (0.06)

0.86

V -0.02 0.32 1.00 (0.05) (0.03)

-0.53 11.00

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26 Population Discrepancy Function Value (F0) = 45.19

90 Percent Confidence Interval for F0 = (43.60 ; 46.82) Root Mean Square Error of Approximation (RMSEA) = 0.28 90 Percent Confidence Interval for RMSEA = (0.27 ; 0.28) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.00

Method of Estimation: Two-stage Least Squares Correlation Matrix of Independent Variables

BI EOU I RD OQ JR --- --- --- --- --- ---

BI 1.00

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27 EOU 0.64 1.00

I 0.15 0.03 1.00

RD 0.39 0.38 0.54 1.00

OQ 0.56 0.40 0.11 0.52 1.00

JR 0.81 0.35 0.43 0.47 0.50 1.00

SN -0.05 -0.58 -0.34 -0.26 -0.25 -0.08

U 0.78 0.78 0.26 0.33 0.38 0.62

V 0.42 0.41 -0.06 0.28 0.57 0.36

SN U V --- --- --- SN 1.00

U -0.35 1.00

V -0.22 0.36 1.00

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28

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29

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30