Results 11  20
of
593
A linear nongaussian acyclic model for causal discovery
 J. Machine Learning Research
, 2006
"... In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to ..."
Abstract

Cited by 54 (23 self)
 Add to MetaCart
In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuousvalued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have nonGaussian distributions of nonzero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any prespecified timeordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear NonGaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and realworld data.
Chain Graph Models and their Causal Interpretations
 B
, 2001
"... Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultim ..."
Abstract

Cited by 48 (4 self)
 Add to MetaCart
Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...
A Scaled Difference Chisquare Test Statistic for Moment Structure Analysis
"... A family of scaling corrections aimed to improve the chisquare approximation of goodnessoffit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, SatorraBentler's (SB) scaling corrections are available in ..."
Abstract

Cited by 45 (0 self)
 Add to MetaCart
A family of scaling corrections aimed to improve the chisquare approximation of goodnessoffit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, SatorraBentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say M 0 implies on a less restricted one M 1 .IfT 0 and T 1 denote the goodnessoffit test statistics associated to M 0 and M 1 , respectively, then typically the difference T d = T 0 ; T 1 is used as a chisquare test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models M 0 and M 1 . As in the case of the goodnessoffit test, it is of interest to scale the statistic T d in order to improveitschisquare approximation in realistic, i.e., nonasymptotic and nonn...
A critical review of construct indicators and measurement model misspecificaPLS Path Modeling – A Software Review 21 tion in marketing and consumer research
 Journal of Consumer Research
, 2003
"... A review of the literature suggests that few studies use formative indicator measurement models, even though they should. Therefore, the purpose of this research is to (a) discuss the distinction between formative and reflective measurement models, (b) develop a set of conceptual criteria that can b ..."
Abstract

Cited by 44 (0 self)
 Add to MetaCart
A review of the literature suggests that few studies use formative indicator measurement models, even though they should. Therefore, the purpose of this research is to (a) discuss the distinction between formative and reflective measurement models, (b) develop a set of conceptual criteria that can be used to determine whether a construct should be modeled as having formative or reflective indicators, (c) review the marketing literature to obtain an estimate of the extent of measurement model misspecification in the field, (d) estimate the extent to which measurement model misspecification biases estimates of the relationships between constructs using a Monte Carlo simulation, and (e) provide recommendations for modeling formative indicator constructs. It has been more than two decades since Churchill (1979), Bagozzi (1980), Peter (1981), and Anderson and Gerbing (1982), among others, criticized the field of marketing for failing to pay enough attention to construct validity and associated measurement issues. A good example of this concern
Graphs, Causality, And Structural Equation Models
, 1998
"... Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. ..."
Abstract

Cited by 44 (14 self)
 Add to MetaCart
Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.
The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis
 Psychological Methods
, 1996
"... Monte Carlo computer simulations were used to investigate the performance of three X 2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood)~2 (ML), Browne's asymptotic distribution free X 2 (ADF), and the SatorraBentler rescaled X 2 (SB) were examined under varyi ..."
Abstract

Cited by 42 (1 self)
 Add to MetaCart
Monte Carlo computer simulations were used to investigate the performance of three X 2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood)~2 (ML), Browne's asymptotic distribution free X 2 (ADF), and the SatorraBentler rescaled X 2 (SB) were examined under varying conditions of sample size, model specification, and multivariate distribution. For properly specified models, ML and SB showed no evidence of bias under normal distributions across all sample sizes, whereas ADF was biased at all but the largest sample sizes. ML was increasingly overestimated with increasing nonnormality, but both SB (at all sample sizes) and ADF (only at large sample sizes) showed no evidence of bias. For misspecified models, ML was again inflated with increasing nonnormality, but both SB and ADF were underestimated with increasing nonnormality. It appears that the power of the SB and ADF test statistics to detect a model misspecification is attenuated given nonnormally distributed data. Confirmatory factor analysis (CFA) has become an increasingly popular method of investigating the structure of data sets in psychology. In contrast to traditional exploratory factor analysis that does not place strong a priori restrictions on the structure of the model being tested, CFA requires the investigator to specify both the number of factors
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
Abstract

Cited by 35 (16 self)
 Add to MetaCart
The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
How good is good enough in path analysis of fMRI data? Neuroimage 2000
"... This paper is concerned with the problem of evaluating goodnessoffit of a path analytic model to an interregional correlation matrix derived from functional magnetic resonance imaging (fMRI) data. We argue that model evaluation based on testing the null hypothesis that the correlation matrix predi ..."
Abstract

Cited by 33 (1 self)
 Add to MetaCart
This paper is concerned with the problem of evaluating goodnessoffit of a path analytic model to an interregional correlation matrix derived from functional magnetic resonance imaging (fMRI) data. We argue that model evaluation based on testing the null hypothesis that the correlation matrix predicted by the model equals the population correlation matrix is problematic because P values are conditional on asymptotic distributional results (which may not be valid for fMRI data acquired in less than 10 min), as well as arbitrary specification of residual variances and effective degrees of freedom in each regional fMRI time series. We introduce an alternative approach based on an algorithm for automatic identification of the best fitting model that can be found to account for
Bayesian model selection in structural equation models
, 1993
"... A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, whe ..."
Abstract

Cited by 29 (10 self)
 Add to MetaCart
A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, when appropriate, and so enables us to take account, both informally and formally, of uncertainty about model structure when making inferences about quantities of interest. The approach tends to select simpler models than strategies based on multiple Pvaluebased tests. It may thus help to overcome the criticism of structural