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## Quasi Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects

Citations: | 14 - 0 self |

### Citations

4095 |
Multiple regression: Testing and interpreting interactions, Sage Publications
- Aiken, West
- 1991
(Show Context)
Citation Context ...& Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (=-=Aiken & West 1991-=-; Busemeyer & Jones 1983; Cohen & Cohen 1975; Jaccard, Turisi & Wan 1990), and different ad-hoc estimation approaches have been developed. Hayduk (1987) established the estimation of an elementary int... |

3684 |
Applied multiple regression/correlational analysis for the behavioral sciences (3rd ed.).
- Cohen, Cohen, et al.
- 2003
(Show Context)
Citation Context ... 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; Busemeyer & Jones 1983; =-=Cohen & Cohen 1975-=-; Jaccard, Turisi & Wan 1990), and different ad-hoc estimation approaches have been developed. Hayduk (1987) established the estimation of an elementary interaction model with one latent product term ... |

2912 |
Understanding Attitudes and Predicting Social Behaviour
- Ajzen, Fishbein
- 1980
(Show Context)
Citation Context ...l researchers have called for estimation methods for nonlinear latent variable models, and numerous substantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; =-=Ajzen & Fishbein 1980-=-; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has bee... |

2380 |
Belief, Attitude, Intention and Behavior: An Introduction to Theory and Research
- Fishbein, Ajzen
- 1975
(Show Context)
Citation Context ...dels, and numerous substantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; =-=Fishbein & Ajzen 1975-=-; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; Busemeyer & Jon... |

832 |
Job demands, job decision latitude, and mental strain: Implications for job redesign.
- Karasek
- 1979
(Show Context)
Citation Context ...tantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; =-=Karasek 1979-=-; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; Busemeyer & Jones 1983; Cohen... |

726 |
EQS: Structural equations programming manual.
- Bentler
- 1995
(Show Context)
Citation Context ...quations, and they are measured with errors by indicator variables in a measurement model. By the development of software packages for covariance structure analysis such as Amos (Arbuckle 1997), EQS (=-=Bentler 1995-=-; Bentler & Wu 1993), LISREL (Jöreskog & Sörbom 1993, 1996a), or Mplus (Muthén & Muthén 1998-2001), SEM has become available to a large community of researchers. While ordinary SEM incorporates linear... |

485 |
Mplus user’s guide.
- Muthén, Muthén
- 1998
(Show Context)
Citation Context ...model. By the development of software packages for covariance structure analysis such as Amos (Arbuckle 1997), EQS (Bentler 1995; Bentler & Wu 1993), LISREL (Jöreskog & Sörbom 1993, 1996a), or Mplus (=-=Muthén & Muthén 1998-=--2001), SEM has become available to a large community of researchers. While ordinary SEM incorporates linear relationships among latent variables, models with nonlinear structural equations have recen... |

462 |
Beyond the two disciplines of scientific psychology.
- Cronbach
- 1975
(Show Context)
Citation Context ...hods for nonlinear latent variable models, and numerous substantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; =-=Cronbach 1975-=-; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological pe... |

449 |
Analysis of Numerical Methods
- Isaacson, Keller
- 1966
(Show Context)
Citation Context ...ters vector θ by application of standard numerical methods. Technically, this maximization is executed in two stages: In the first stage of the maximization process, the single-step iteration method (=-=Isaacson & Keller 1966-=-; Schwarz 1993) is used; in the second stage, the Newton-Raphson algorithm is applied. The maximization algorithm is programmed in Delphi Pascal program code and executed on an IBM compatible computer... |

375 | Interaction Effects in Multiple Regression - Jaccard, Turrisi, et al. - 1990 |

232 |
Aptitudes and instructional methods: A handbook for research on interactions.
- Cronbach, Snow
- 1977
(Show Context)
Citation Context ...ear latent variable models, and numerous substantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; =-=Cronbach & Snow 1977-=-; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & Wes... |

185 | Coefficient Models. - Longford - 1993 |

156 |
Computing the distribution of quadratic forms in normal variables,
- Imhof
- 1961
(Show Context)
Citation Context ... general, which also implies that the vector yt of indicator variables is nonnormally distributed. The distribution type of ηt has been investigated for special cases in the literature (Gurland 1955; =-=Imhof 1961-=-; Shah 1963; Press 1966), but, as Johnson and Kotz (1970) point out, these 6srepresentations of the nonnormal density function are neither theoretically nor practically useful because of their complic... |

133 |
AMOS user’s guide version 3.6.
- Arbuckle
- 1997
(Show Context)
Citation Context ...lated in structural equations, and they are measured with errors by indicator variables in a measurement model. By the development of software packages for covariance structure analysis such as Amos (=-=Arbuckle 1997-=-), EQS (Bentler 1995; Bentler & Wu 1993), LISREL (Jöreskog & Sörbom 1993, 1996a), or Mplus (Muthén & Muthén 1998-2001), SEM has become available to a large community of researchers. While ordinary SEM... |

119 |
An Introduction to Multivariate Statistics
- Srivastava, G
- 1979
(Show Context)
Citation Context ...ons of the nonnormal density function are neither theoretically nor practically useful because of their complicated structure. The characteristic function of ηt or yt can be expressed in closed form (=-=Srivasta & Khatri 1979-=-), but it is not possible to derive the density function from the characteristic function by integrating out the transform variable, because the integral cannot be solved in an analytically closed for... |

118 | Estimating the nonlinear and interactive effects of latent variables. - Kenny, Judd - 1984 |

113 | Tenacious Goal Pursuit and Flexible Goal Adjustment: Explications and Age-Related Analysis of Assimilation and - Brandtstädter, Renner - 1990 |

99 |
Interdependence, Contracting, and Relational Behavior in Marketing Channels,"
- Lusch, Brown
- 1996
(Show Context)
Citation Context ...es in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; =-=Lusch & Brown 1996-=-; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; Busemeyer & Jones 1983; Cohen & Cohen 1975; Jacca... |

97 | Structural equation modeling with LISREL. - Hayduk - 1987 |

94 |
PRELIS 8: User’s reference guide. Chicago: Scientific Software.
- Jöreskog, Sörbom
- 1993
(Show Context)
Citation Context ...improved by Jaccard and Wan (1995), Jöreskog and Yang (1996, 1997), and Yang Jonsson (1997) who used nonlinear parameter constraints for estimation of the elementary interaction model under LISREL 8 (=-=Jöreskog & Sörbom 1996-=-a). Simulation studies show that the LISREL-ML estimation procedure can be used for parameter estimation of the elementary interaction model (Yang Jonsson 1997), 2sbut applicability seems to be limite... |

75 | Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: multiple indicator and structural equation approaches. - SONG, Jaccard, et al. - 1995 |

71 |
Analysis of multiplicative combination rules when the causal variables are measured with error.
- Busemeyer, Jones
- 1993
(Show Context)
Citation Context ...in & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; =-=Busemeyer & Jones 1983-=-; Cohen & Cohen 1975; Jaccard, Turisi & Wan 1990), and different ad-hoc estimation approaches have been developed. Hayduk (1987) established the estimation of an elementary interaction model with one ... |

69 |
Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In
- Jöreskog, Yang
- 1996
(Show Context)
Citation Context ...plies that α = -tr(ΩΦ). This restriction does not limit the applicability of the model in practice. The nonlinear structural equation implies that the vector yt is nonnormally distributed in general (=-=Jöreskog & Yang 1996-=-; Klein & Moosbrugger 2000). 3. QUASI-ML ESTIMATION PROCEDURE The major characteristic of a nonlinear structural equation model lies in the fact that the latent dependent variable ηt given by the stru... |

67 |
Maximum likelihood estimation of latent interaction effects with the LMS method.
- Klein, Moosbrugger
- 2000
(Show Context)
Citation Context ...n adjustment for bias (Yang-Wallentin & Jöreskog 2001). Moreover, simulation studies for the elementary interaction model indicate that the LISREL parameter estimators do not have maximum efficiency (=-=Klein & Moosbrugger 2000-=-; Schermelleh-Engel et al. 1998). As an alternative to covariance structure analysis, a two-stage least squares (2SLS) estimation technique has been developed by Bollen (1995, 1996) and Bollen and Pax... |

64 | A parsimonious estimating technique for interaction and quadratic latent variables”, - Ping - 1995 |

61 | S.: Continuous univariate distributions – 2 - Johnson, Kotz - 1970 |

56 |
Robust properties of likelihood ratio tests (Corr: V69 p492). Biometrika 69
- Kent
- 1982
(Show Context)
Citation Context ...ers and parameter vector Θ 0 , the log quasi-likelihood ratio L = -2(l( 0 Θˆ ) - l( Θˆ )) converges in distribution to ∑ λ = r k 1 9 k Wk when sample size increases (Carroll et al. 1995, pp. 265-267; =-=Kent 1982-=-). The W1,...,Wr are independently 2 χ1 -distributed, and λ1,...,λr are calculated from the above matrices H and J. In the Quasi-ML method, the quantiles of the distribution of the test statistic are ... |

53 | A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis–Hastings algorithm. - Arminger, Muthén - 1998 |

50 | EQS user’s guide.
- Bentler, Wu
- 1995
(Show Context)
Citation Context ...they are measured with errors by indicator variables in a measurement model. By the development of software packages for covariance structure analysis such as Amos (Arbuckle 1997), EQS (Bentler 1995; =-=Bentler & Wu 1993-=-), LISREL (Jöreskog & Sörbom 1993, 1996a), or Mplus (Muthén & Muthén 1998-2001), SEM has become available to a large community of researchers. While ordinary SEM incorporates linear relationships amon... |

44 |
Prediction of Goal-Directed Behavior: Attitudes, Intentions, and Perceived Behavioral Control.
- I, Madden
- 1986
(Show Context)
Citation Context ...ed for estimation methods for nonlinear latent variable models, and numerous substantive theories in education and psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; =-=Ajzen & Madden 1986-=-; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a me... |

44 | Latent variable interaction and quadratic effect estimation: a two-step technique using structural equation analysis”, - Ping - 1996 |

34 | An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations - BOLLEN - 1996 |

29 |
New features
- Jöreskog, Sörbom
- 1996
(Show Context)
Citation Context ...s by indicator variables in a measurement model. By the development of software packages for covariance structure analysis such as Amos (Arbuckle 1997), EQS (Bentler 1995; Bentler & Wu 1993), LISREL (=-=Jöreskog & Sörbom 1993-=-, 1996a), or Mplus (Muthén & Muthén 1998-2001), SEM has become available to a large community of researchers. While ordinary SEM incorporates linear relationships among latent variables, models with n... |

26 |
Behavior and attitude: Some people are more consistent than others.
- Snyder, Tanke
- 1976
(Show Context)
Citation Context ...psychology call for analysis of nonlinear models (Ajzen 1987; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; =-=Snyder & Tanke 1976-=-). Also, a need for nonlinear extensions of ordinary SEM has been expressed from a methodological perspective (Aiken & West 1991; Busemeyer & Jones 1983; Cohen & Cohen 1975; Jaccard, Turisi & Wan 1990... |

20 |
Estimation for polynomial structural equation models
- Wall, Amemiya
- 2000
(Show Context)
Citation Context ...method is compared to three alternative techniques, the LMS method (Klein 2000; Klein & Moosbrugger 2000), the LISREL-ML method (Jöreskog & Yang 1996, 1997; Yang Jonsson 1997), and the 2SMM approach (=-=Wall & Amemiya 2000-=-). In the second Monte-Carlo study, a model with four latent nonlinear effects demonstrates the general applicability of the new Quasi-ML method to complex nonlinear latent variable models. The comple... |

19 | Structural equation models that are nonlinear in latent variables: A least squares estimator. - Bollen - 1995 |

17 | Applied Statistics Algorithms - Griffiths, Hill - 1985 |

17 |
LISREL 7: A guide to the program applications (2nd ed.).
- Jöreskog, Sörbom
- 1989
(Show Context)
Citation Context ... estimation approaches have been developed. Hayduk (1987) established the estimation of an elementary interaction model with one latent product term proposed by Kenny and Judd (1984). Using LISREL 7 (=-=Jöreskog & Sörbom 1989-=-), they formed products of indicators for measuring the latent product term. Two-step LISREL approaches for this elementary model were proposed by Moosbrugger, Frank, and Schermelleh-Engel (1991) and ... |

14 | Latent variable regression: A technique for estimating interaction and quadratic coefficients. - Ping - 1996 |

14 |
Linear Combinations of Noncentral Chi-Square Variates
- Press
- 1966
(Show Context)
Citation Context ...plies that the vector yt of indicator variables is nonnormally distributed. The distribution type of ηt has been investigated for special cases in the literature (Gurland 1955; Imhof 1961; Shah 1963; =-=Press 1966-=-), but, as Johnson and Kotz (1970) point out, these 6srepresentations of the nonnormal density function are neither theoretically nor practically useful because of their complicated structure. The cha... |

14 |
Estimating nonlinear effects using a latent moderated structural equations approach
- Schermelleh-Engel, Klein, et al.
- 1998
(Show Context)
Citation Context ...g-Wallentin & Jöreskog 2001). Moreover, simulation studies for the elementary interaction model indicate that the LISREL parameter estimators do not have maximum efficiency (Klein & Moosbrugger 2000; =-=Schermelleh-Engel et al. 1998-=-). As an alternative to covariance structure analysis, a two-stage least squares (2SLS) estimation technique has been developed by Bollen (1995, 1996) and Bollen and Paxton (1998) using instrumental v... |

12 | Two-stage least squares estimation of interaction effects. In - Bollen, Paxton - 1998 |

12 |
Distribution of definite and indefinite quadratic forms
- Gurland
- 1955
(Show Context)
Citation Context ...distributed in general, which also implies that the vector yt of indicator variables is nonnormally distributed. The distribution type of ηt has been investigated for special cases in the literature (=-=Gurland 1955-=-; Imhof 1961; Shah 1963; Press 1966), but, as Johnson and Kotz (1970) point out, these 6srepresentations of the nonnormal density function are neither theoretically nor practically useful because of t... |

9 | EQS and LISREL examples using survey data - Ping - 1998 |

8 |
Distribution of definite and of indefinite quadratic forms from a non-central normal distribution,”
- Shah
- 1963
(Show Context)
Citation Context ...ich also implies that the vector yt of indicator variables is nonnormally distributed. The distribution type of ηt has been investigated for special cases in the literature (Gurland 1955; Imhof 1961; =-=Shah 1963-=-; Press 1966), but, as Johnson and Kotz (1970) point out, these 6srepresentations of the nonnormal density function are neither theoretically nor practically useful because of their complicated struct... |

5 | Estimation of interaction models using the augmented moment matrix: Comparison of asymptotic standard errors - Jöreskog, Yang - 1997 |

5 | Non-linear structural equation models: Simulation studies of the KennyJudd model. Unpublished doctoral dissertation - Jonsson - 1997 |

3 |
Moderatormodelle. Verfahren zur Analyse von Moderatoreffekten in Strukturgleichungsmodellen [Moderator models. Methods for the analysis of moderator effects in structural equation models
- Klein
- 2000
(Show Context)
Citation Context ...on studies for the elementary interaction model indicate that LMS provides efficient parameter estimators and a reliable model difference test, and they show no indication of bias of standard errors (=-=Klein 2000-=-; Klein & Moosbrugger 2000; Schermelleh-Engel et al. 1998). But, although models with multiple latent product terms can be analyzed with the LMS method, the method can become computationally too inten... |

2 |
Attitudes, traits, and actions: Dipositional prediction of behavior in personality and social psychology
- Ajzen
- 1987
(Show Context)
Citation Context ...tion. Several researchers have called for estimation methods for nonlinear latent variable models, and numerous substantive theories in education and psychology call for analysis of nonlinear models (=-=Ajzen 1987-=-; Ajzen & Fishbein 1980; Ajzen & Madden 1986; Cronbach 1975; Cronbach & Snow 1977; Fishbein & Ajzen 1975; Karasek 1979; Lusch & Brown 1996; Snyder & Tanke 1976). Also, a need for nonlinear extensions ... |

2 | Estimation of nonlinear structural equation models using empirical characteristic functions - Blom, Christoffersson - 2001 |

2 |
Measurement error in nonlinear models (1 st ed
- Carroll, Ruppert, et al.
- 1995
(Show Context)
Citation Context ...dicator vector (xt´, yt´)´ by a nonnormal density f*(x, y), which is a product of a normal and a conditionally normal density. This approximation makes use of the concept of variance function models (=-=Carroll et al. 1995-=-), where the mean and variance function of a dependent variable conditional on the independent variables is specified. The maximization of the quasi-loglikelihood function derived from the approximati... |

2 |
PRELIS 2: User's guide. Chicago: Scientific Software
- Jöreskog, Sörbom
- 1996
(Show Context)
Citation Context ...improved by Jaccard and Wan (1995), Jöreskog and Yang (1996, 1997), and Yang Jonsson (1997) who used nonlinear parameter constraints for estimation of the elementary interaction model under LISREL 8 (=-=Jöreskog & Sörbom 1996-=-a). Simulation studies show that the LISREL-ML estimation procedure can be used for parameter estimation of the elementary interaction model (Yang Jonsson 1997), 2sbut applicability seems to be limite... |

1 | Physische Leistungsvariablen als Indikatoren für die Diagnose „Klimakterium Virile“ (Physical efficiency variables as indicators for the diagnosis of ‘climacterium virile - Degenhardt, Schmidt - 1994 |

1 |
Frankfurter Körperkonzept-Skalen (Frankfurt bodily self-concept scales
- Deusinger
- 1998
(Show Context)
Citation Context ...tively perceived fitness (ξ1t) refers to the self-evaluation of the effectiveness with which one’s body is functioning. It was measured by a split scale (x1, x2) of self-concept of bodily efficiency (=-=Deusinger 1998-=-). The objective fitness (ξ2t) refers to the objective level of fitness. It was measured by lung volume (x3). Flexibility in goal adjustment (ξ3t) addresses the fact that individuals are more or less ... |

1 | Stochastische Methoden (Stochastic Methods - Krickeberg, Ziezold - 1988 |

1 | Zur Überprüfung von latenten Moderatoreffekten mit linearen Strukturgleichungsmodellen (Estimating latent interaction effects in structural equation models). Zeitschrift für Differentielle und Diagnostische Psychologie - Moosbrugger, Frank, et al. - 1991 |

1 | Verlust körperlicher Leistungsfähigkeit: Bewältigung des Alterns bei Männern im mittleren Lebensalter (Loss of bodily efficacy: The coping of aging for men of medium age - Thiele - 1998 |