8th JACET Vocabulary Acquisition Research Group Conference (December 10, 2011)

An introduction to structuralequation modeling for vocabulary
research
Yo In’nami
Toyohashi University of Technology
innami@las.tut.ac.jp
www7b.biglobe.ne.jp/~koizumi/Innami/top-english.html
1Overview• SEM basics• SEM demo
• Applications2• Structural equation modeling (SEM)– Also called covariance structure analysis or
simultaneous equation modeling– A statistical technique for examining thenature of the relationships among observed
and latent variables that applies a
confirmatory, hypothesis-testing approach to
the data (e.g., Byrne, 2006)– Regression + factor analysis– Encompasses ANOVA, ANCOVA, CFA,
regression…
– Suitable for visually presenting study findings3Observed variable (e.g.,test/questionnaire score)(rectangle)

Latent variable (i.e.,construct/factor) (oval)

Measurement
error(circle)

Shiotsu &Weir (2007)

Correlation(two-wayarrow)

Regression(one-wayarrow)

4The diagram was displayed at theworkshop.

Tseng, Dörnyel,& Schmitt (2006,p. 93)

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The diagram was displayed at theworkshop.

Mizumoto &Takeuchi (inpress)

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Koizumi &In’nami (inpreparation)7• Four advantages of SEM (Byrne, 2006)– SEM takes a confirmatory, hypothesis-testing approach to the data, incontrast to traditional analysis, such as exploratory factor analysis, whereanalysis is data driven.
– SEM is designed to correct for measurement errors of variables. The
results allow a researcher to interpret the relationship among variables,
separating the measurement errors.
– SEM can analyze both unobserved (i.e., latent) and observed
variables. This contrasts with path analysis that enables researchers tomodel only observed variables. Latent variables are used to define factors
or constructs.
– Multivariate relations or indirect effects can be analyzed using SEM,
whereas no other statistical methods can easily do this. Investigation into
multivariate relations may include models where correlations arehypothesized only among a certain set of variables. Investigating indirect
effects may include determining whether an independent variable directly
affects a dependent variable or whether it does so through a mediatingvariable. Path analysis can be used to model these multivariate relations
or indirect effects with observed variables, but it cannot be used to conduct
analyses using unobserved variables.
8• Five steps involved in an SEM application(Bollen & Long, 1993)– Model specification– Model identification– Parameter estimation• E.g., Maximum likelihood– Model fit• E.g., CFI– Model respecification
9• Requirements:– Sample size: 100–200+– Normality• Univariate skewness & kurtosis• Multivariate kurtosis– Missing data10

Overview• SEM basics• SEM demo
• Applications

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SEM demo• Koizumi & In’nami (in preparation)– Examining the uni-factor structure ofvocabulary knowledge– SPSS & Amos
– Sample size: 100–200+ (224)– Normality• Univariate skewness & kurtosis (OK)• Multivariate kurtosis (OK)– Missing data (No missing data)
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Create theinput data
file in 13
SPSS/Excel

Draw themodel using
Amos 14

Read theinput filefrom SPSS
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Run themodel16

Univariate normality: (1)
Skewness & kurtosisis, c.r.
(critical ratio) ≤ ±1.96 (or 3.29).
(2) Better to examine thehistogram and the skewness &kurtosis statistics rather than tocalculate their significance (N ≥200; Field, 2005, p. 72).

Multivariate normality: (1)c.r. (critical ratio) ≤ ±1.96(or 3.29), (2) c.r. values >5.00 indicate nonnormal
distribution (Bentler, 2005,p. 106; Byrne, 2010, p.
104 ).
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Multivariate normality:
Mahalanobis distanceless than 13.816 (fordf = 2, p < .001, χ2 =13.816)
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1 orabove,good; ifnegative,the model
can’t betested.

19All paths are
statisticallysignificant.

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21

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Χ2 (CMIN)

dfpCFI

TLI

RMSEA(90% CI)

pclosefit

SRMR

H0OurModel
3.846

Criteria

2.146

.997

0.990

nonsig

> .95

Near
1.00

0.064
(0.000,0.161)

.299

.014

=< 0.05> .05=< .08This tests the null
hypothesis that the
population RMSEA is nogreater than .05.
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How to calculate
SRMR• Run the model with theSRMR box left open andblank.

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SEM results are (generally) reproducible even without
the raw data, given access to (1) correlations & SDs[+means]) or (2) variances/covariances. This suggeststhat we can reproduce previous studies to see if themodel was correctly analyzed and/or examine
alternative models not tested in the primary study (seeIn’nami & Koizumi, 2010, for further details).

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26

Left; raw
data
input.
Right; r,M, SD
input
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Overview• SEM basics• SEM demo• Applications

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Crosssectional
investigation intogrowth

Is there a high correlation between sizeand depth (Is vocabulary knowledge aunitary construct)? Is the structure
different across learners of different
proficiency (novice, intermediate,advanced)? (multi-sample model)

Does the strength of association
between size and depth vary suchthat a model of separate size anddepth is more appropriate?
(hierarchical/higher-order model)

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Longitudinal
investigation into
growthDoes this model hold as
learners expand their
vocabulary knowledge? Are
there any moderating
variables? (latent growthmodel)
Year 1

Year 2

Year 330

• The diagram was displayed at the workshop.

Tseng & 31
Schmitt, (2008)• The diagram was displayed at the workshop.

Tremblay &Gardner (1995)

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• The diagram was displayed at the workshop.

Yashima (2002) 33

• The diagram was displayed at the workshop.

Matsumura (2003);
latent growth model34• The diagram was displayed at the workshop.

Llosa (2007);
hierarchical/higher-order model

35• The tables were displayed at the workshop.

In’nami & Koizumi, 201136• The table was displayed at the workshop.

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Software• GUI = graphic user interface.
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SEMNET• http://www2.gsu.edu/~mkteer/semnet.html

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References•••••••••

Bentler, P. M. (2005). EQS 6 structural equations program manual. Encino, CA:
Multivariate Software.
Bollen, K. A., & Long, J. S. (1993). Introduction. In K. A. Bollen & J. S. Long (Eds.),
Testing structural equation models (pp. 1–9). Newbury Park, CA: Sage.
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York:Guilford.
Byrne, B. M. (2010). Structural equation modeling with AMOS: Basic concepts,applications, and programming (2nd ed.). Mahwah, NJ: Erlbaum.
Byrne, B. M. (2006). Structural equation modeling with EQS: Basic concepts,applications, and programming (2nd ed.). Mahwah, NJ: Erlbaum.
Byrne, B. M. (2011). Structural equation modeling with Mplus: Basic concepts,applications, and programming. Mahwah, NJ: Erlbaum.
Field, A. (2005). Discovering statistics using SPSS (2nd ed.). London: Sage.
In’nami, Y., & Koizumi, R. (2010). Can structural equation models in second language
testing and learning research be successfully replicated? International Journal ofTesting, 10, 262–273.
In’nami, Y., & Koizumi, R. (2011). Structural equation modeling in language testing
and learning research: A review. Language Assessment Quarterly, 8, 250–276.

40References••••••••••Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York:Guilford.
Koizumi, R., & In’nami, Y. (in preparation).
Llosa, L. (2007). Validating a standards-based classroom assessment of English proficiency: A
multitrait-multimethod approach. Language Testing, 24, 489–515.
Matsumura, S. (2003). Modelling the relationships among interlanguage pragmatic development,
L2 proficiency, and exposure to L2. Applied Linguistics, 24, 465–491.
Mizumoto, A., & Takeuchi, O. (in press). Adaptation and validation of self-regulating capacity invocabulary learning scale. Applied Linguistics.
Shiotsu, T., & Weir, C. J. (2007). The relative significance of syntactic knowledge and vocabulary
breadth in the prediction of reading comprehension test performance. Language Testing, 24, 99–128.
Tremblay, P. F., & Gardner, R. C. (1995). Expanding the motivation construct in language
learning. Modern Language Journal, 79, 505–518.
Tseng, W.-T., Dornyei, Z., & Schmitt, N. (2006). A new approach to assessing strategic learning:
The case of self-regulation in vocabulary acquisition. Applied Linguistics, 27, 78–102.
Tseng, W.-T., & Schmitt, N. (2008). Toward a model of motivated vocabulary learning: A
structural equation modeling approach. Language Learning, 58, 357–400.
Yashima, T. (2002). Willingness to communicate in a second language: The Japanese EFL
context. Modern Language Journal, 86, 54–66.

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