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# Path analysis with manifest variables

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### Path analysis with manifest variables

1. 1. PATH ANALYSIS WITH MANIFEST VARIABLES<br />Carlos Gabriel Contreras Msc<br />Department of statistics<br />University of California Los Angeles.<br />
2. 2. Introduction: the basic of path analysis<br />Path analysis can be used to test theoretical models that specify causal relationship between a number of observed variables.<br />Path Analysis determines whether the theoretical model successfully accounts for the actual relationship observed in the sample data.<br />In SAS, the ouput of the CALIS procedure provides indices that indicate whether the model, as a whole, fits the data, as quell as significance tests for specific causal paths.<br />When a model provides a relatively poor fit to the data, additional retults from PROC CALIS can be used to modify the model and improve its fit.<br />
3. 3. Introduction: the basic of path analysis<br />This presentation deals only with causal models in which all variables are manifest (observed) variables.<br />It does not deal with path models that specify causal relationship between LATENT (unobserved) variables (Such models are often called LISREL type. <br />
4. 4. Some simple path diagrams<br />When studying complex phenomena, if often becomes clear that a given outcome variable of interest is actually influenced by a variety of other variables, few outcome variables of any importance are causally determined by just one variable.<br />a theorist in industrial psychology who believes that an employee’s work performance (the outcome variable of interest) is influenced by the following four variables<br />The employee’s level of intelligence<br />The employee’s level of work motivation.<br />Work place norms<br />Supervisory support.<br />
5. 5. Intelligence<br />Motivation<br />Work performance<br />Work place norms<br />Supervisory support<br />
6. 6. Continued.<br />Intelligence, motivation, work place norms, and supervisory support are all antecedent variables within this framework, as they are clearly predicted to precedent and have a causal effect on work performance. Similarly, work performance is the consequent variable in the model, as it is said to be affected by these antecedent variables.<br />In the path analysis literature, many refer to antecedent variables as independent variables, and consequent variables as dependent variables (although these terms obviously do not have the same meaning in path analysis research, which is correlational in nature, as they have in experimental research)<br />
7. 7. Continued.<br />The boxes in the path are connected to one another by mean of straight, single-headed arrows and curved, double-headed arrows. In the path analysis literature, straight, single-headed arrow is generally used to represent a unidirectional causal path in a path diagram. The arrow originates at the variable exerting the causal influence (the independent variable), and the arrow points toward the variable being affected (the dependent variable). <br />In contrast, a curved double-headed arrow connecting two variables represent a simple covariance or correlation, between the variables. <br />A curved arrow connecting two variables means that the two variables are expected to co vary, but that no hypothesis is made regarding any causal influence between them.<br />
8. 8. Intelligence<br />Motivation<br />Work place norms<br />Work performance<br />Supervisory support<br />
9. 9. Continued.<br />The anterior diagram includes the same four variables discussed earlier, but they are arranged in a somewhat different causal sequence. Most notably, worker motivation is now viewed as a mediator variable<br />Mediator variable is a variable that mediates, or coveys, the effect of an antecedent variable onto a consequent variable. <br />
10. 10. ENDOFENOUS VERSUS EXOGENOUS VARIABLES.<br />In path analysis, a distinction is made between endogenous variables and exogenous variables. An endogenous variables is one whose variability is predicted to be causally affected by other variables in the model.<br />Any variables that has a straight, single-headed arrow pointing at it is an endogenous variable. Work performance in previous examples are clearly a endogenous variable.<br />On the other hand, are constructs that are influenced only by variables that lie outside of the causal model. Exogenous variables do not have any straight, single-headed arrow pointing at them. Intelligence, norms, and support are all exogenous variables.<br />
11. 11. MANIFEST VERSUS LATENT VARIABLES.<br />A manifest variables is one that is directly measured or observed in the course of an investigation, while a latent variable is a hypothetical construct that is no directly measured or observed. For example, scores on the Weschler Adult Intelligence Scale WAIS, is a manifest variable; it is possible to directly determinate exactly where each subject stands on this variable. <br />On the other hand, intelligence may ne thought of as a latent variable; it is a construct that is presumed to exist, although is cannot be directly observed.<br />In the diagram, manifest variables are represented by rectangles<br />
12. 12. RECURSIVE VERSUS NONRECURSIVE MODELS.<br />A recursive model is on in which causation flows in only one direction.<br />In a recursive model. A consequent variable never exerts causal influence (either directly or indirectly) on an antecedent variable that first exerts causal influence on it. In other words, recursive models are unidirectional.<br />In contrast, in a no recursive path model, causation may flow in more that one direction, an a variable may have direct or indirect effect on another variable that preceded it in the causal chain.<br />
13. 13. Necessary conditions in path models: Interval or ratio level measurement.<br />All endogenous variables should ne assessed on an interval or ratio level of measurement. Exogenous variables should also be on an interval or ratio, although exogenous variables may be assessed at a nominal level if they are dummy coded. Alternative procedures for situations in which these assumptions are violated have been discussed elsewhere.<br />
14. 14. Necessary conditions in path models: minimal number of values.<br />Endogenous variables should be continuous and should assume a minimum of four values.<br />
15. 15. Necessary conditions in path models: Normally distributed data<br />Although parameter estimated may be correct with non normal data, the statistical test used with PROC CALIS in SAS (Such as the model Chi square test and significance test for path coefficients) assume a multivariate normal distribution. <br />Is has been argued, however, that the maximum likelihood and generalized least squares estimation procedures appear to be fairly robust against moderate violation of this assumption.<br />
16. 16. Necessary conditions in path models: Linear and additive relationships.<br />Relationships between variables should be linear and additive (that is, relationships between independent and dependent variables should not be curvilinear or interactive)<br />
17. 17. Necessary conditions in path models: Absence of multicollinearity.<br />Variables should be free of multicollinearity. Multicollinearity is a condition in which one or more variables exhibit very strong correlation.<br />
18. 18. Necessary conditions in path models: Absence of measurement error.<br />All independent variables should be measured without error. This means that any independent manifest variable that is analyzed should be a perfectly reliable indicator of the underlying construct that it is with variables typically studied in the social sciences, this may be the most frequently violated assumption in the use of path analysis.<br />
19. 19. Necessary conditions in path models: Inclusion of all nontrivial causes.<br />All know nontrivial causes of a model’s endogenous variables should be included in the model as independent variables. <br />
20. 20. Necessary conditions in path models: Minimal number of observation.<br />Path analysis is a large sample procedure; it is best that the analysis is based on at least 200 subject (although results based on fewer subject have certainly been reported in the literature)<br />In addition, there should be ratio of at least 5 subjects for each parameter to be estimated. The total number of parameters is the sum of the: path coefficients, variances, covariances.<br />