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27 Cards in this Set
- Front
- Back
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What are the assumptions one must make in doing a Path Analysis using ML estimation?
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MOEnExx
- Model is correctly specified -Observations are independent - Endogenous variables (DV’s) are normally distributed multivariately - Exogenous variables are not correlated with errors/disturbances and Exogenous variables are measured without error (consistent with model specification)—not unique to ML Violations of these assumptions are the following: 1. Non-normality |
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Define/Describe recursive/nonrecursive path models.
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With Recursive models—
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Define/Describe Correlated errors in path models—which can be treated as recursive (e.g., bow-free vs bow pattern)
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bow free pattern = considered recursive; Path models with correlated Errors
(Disturbances in Kline) for DV’s can be treated as if recursive for purposes of identification if correlated errors are for DV’s with no direct effects between them bow pattern - considered non-recursive See diagrams on page 8 and 9 of class 13 MIGHT WANT TO LOOK THIS UP IN BOOK |
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Define/Describe Comparative Fit Index.
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CFI ranges from 0 to 1, with values closer to 1.00 being indicative of good fit.
The Comparative Fit Index is one of a class of fit statistics known as incremental or comparative fit indexes. All of these indexes asses the relative improvement in fit of the researchers model compared with a baseline model (typically an independence/null model which assumes zero population covariances among the observed variables). -The CFI does NOT assume zero error of approximation, (The error of approximation concerns the lack of fit of the researcher's model to the population covariance matrix). |
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Define/Describe Chi Square model.
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Model Chi Square is also known as the likelihood ratio chi-square or generalized likelihood ratio. The value of chi square for a just identified model generally equals zero and has no degrees of freedom. If chi square equals zero, the model perfectly fits the data (i.e., the predicted correlations and covariances equal their observed counterparts. As the value of chi square increases, the fit of an overidentified model becomes increasingly worse. Chi square is actually a badness of fit index be/c the higher its value, the worse the model's correspondence to the data.
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Discuss the concerns raised by Byrne with using Likert scale items as continuous variables in SEM analysis. What are the concerns and how might they most usefully be addressed and/or minimized?
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Likert scales are used in most SEM applications and are used with ML estimation. Byrne's concerns are represented by the following questions:
AICR + NEG -Are Likert scales really continuous or do they instead represent ordinal categories? -Information is lost when converting continuity to limited number of categories needed for likert scales. -Correlations lowered -Reduction in variance -Normally distributed responses would be helpful -Equal Distance between scale pts may not be present w/ likert. -Greater than 4 categories should be used on your likert scale. I think that this is how you might minimize it: Converting something to a likert scale is likely to have a negligent effect if the Likert scale has >4 categories and the responses are normally distributed; otherwise, parameter estimates are lower and estimates of fit may be affected |
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What is the relationship between correlation and causation? e.g., When can you have a correlation between two variables without one causing the other? When can you have no correlation between two variables, when one does cause the other?
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Why might correlation not equal causation?
SCOT -Spurious (caused by 3rd var) No correlation, when one actually does cause the other: -Curvilinear relationships can yield nonsig r's -Obscured correlation -Timing of measurement is off "Correlation does not imply causation” |
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What are the problems associated with inferring causality from path analysis of cross-sectional data? from path analysis of longitudinal data?
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Problems inferring causality from path analysis of cross sectional data
DEST Direction of causal relationship is hard to specify Experimental verification of cross sect needed Sound theory needed for specification of cross sect, if not, probs. Problems inferring causality from path analysis of longitudinal data Time precedence is hard to establish A T Attrition can make longitudinal difficult Third variables can be hard to control ______ Problems inferring causality from path analysis of cross sectional data Harder to specify direction of causal relationship; harder to establish time precedence Needs to be experimentally or longitudinally verified W/ cross sectional, you need careful specification based on sound theory – if theory is bad or is limited, you’re in trouble. Problems inferring causality from path analysis of longitudinal data Subject attrition can make this type of project difficult May not be able to control for all potential 3rd variables Lack of correlation does not imply lack of causality: |
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What would you expect to see in the residual covariance matrix and in the fit indices if analyzing a saturated path model? Why?
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Just-identified (saturated) path models (PAT)
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What are Kline’s suggested “rules of thumb” for sample size in path analysis? What are the potential problems that can occur if sample size is not adequate?
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Sample size in path models
rules of thumb + SIT |
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How does EQS handle inadmissable values in model estimation (e.g., Heywood cases). What problems can inadmissable values (or condition codes indicate)? How can they be addressed?
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When Heywood cases are evident (inadmissable values such as negative variance, correlations > 1.00), EQS constrains the value of
these parameters and issues a “Condition Code” Inadmissable values (or condition codes) can indicate: SO, HUSB - Small sample size and inadequate measurement - Outliers that distort solution -High correlations that create empirical underidentification -Under-identification -specification errors - Bad start values Inadmissable values (or condition codes) can be addressed by: -looking at residual matrix to see where the model is misspecified -try rescaling variables -examine start values |
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Define/Describe saturated or just-identified model
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-A saturated model may provide a useful baseline for testing other nested models
Just-identified (saturated) path models: PAT |
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What is included in the error or disturbance terms in path analysis?
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In path analysis, Errors and Disturbances are confounded. “Errors”
include both measurement “Error” and “Disturbance” in prediction. It is also important to note: Path models with correlated Errors (Disturbances in Kline) for DV’s can be treated as if RECURSIVE for purposes of identification if: |
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Define/Describe Path Analysis
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Path Analysis models explanatory relationships between observed variables
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Define/Describe Heywood case
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Heywood cases are one of the potential problems in estimation for Path analysis.
Heywood cases = inadmissable values such as negative variance, correlations > 1.00) To deal with heywood values (I think): EQS can constrain the value of these parameters and issues a “Condition Code”. Condition codes/ inadmissable values can be caused by : So, Husb -Small sample size and inadequate measurement -outliers that distort solution -High correlations that create empirical underidentification - Under-identification -specification errors -bad start values |
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Define/Describe Root Mean Square Error of Approximation (RMSEA)
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*RMSEA is a fit index that adjusts for model complexity.*
VALUE of RMSEA should ideally be ≤ .05. The RMSEA measures the ERROR of approximation, and for ths reason it is sometimes referred to as a population based index. (The error of approximation concerns the lack of fit of the researcher's model to the population covariance matrix). The RMSEA approximates a NONCENTRAL chi square distribution, which does NOT require a true NULL hypothesis. The RMSEA is a BADNESS of fit index in that a value of zero indicates the best fit and higher values indicate worse fit. RMSEA is a parsimony adjusted index in that its formula includes a built-in correction for MODEL complexity. |
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Identify the four fit indices. Discuss desirable values and advantages/limitations (e.g., adjustment for model size and complexity)
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1.Chi-Square model
2.Comparative Fit Index (CFI) 3.Root Mean Square Error of Approximation (RMSEA) 4. Standardized Root Mean Square Residual (SMSR) NEED TO ADD DESIREABLE VALUES AND ADVANTAGES/LIMITATIONS FOR EACH OF THESE. |
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Define/Describe Standardized Root Mean Square Residual (SMSR).
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The standardized root mean square residual is based on transforming both the sample covariance matrix and the predicted covariance matrix into correlation matrices.
The SRMR is a measure of the mean absolute correlation residual, the overall difference between the observed and predicted correlations. Values of the SRMR less than 0.10 are generally considered favorable. |
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Describe the two approaches suggested by Kline for model specification/respecification in Path Analysis? What is the ultimate goal of both approaches?
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Specification in Path Analysis (notes):
When doing specification of path models: -Include as many relevant predictors as possible -Be mindful of the fact that Excluded variables—may yield inaccurate estimates of effects in the model -Use variables with good psychometric properties. |
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Define/Describe Lagrange Multiplier Test (LMtest) and values suggesting that a parameter might added to the model to improve fit.
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A modification index is a univariate version of a Lagrange Multiplier.
The value of an LM in the form of a modfidcation index estimates the amount by which the overall model chi square statistic would decrease if a particular fixed to zero path were freely estimated. Thus, the greater the value of a modification index, the better the predicted improvement in overall fit if that path were added to the model. Likewise, a multivariate LM estimates the effect of allowing a set of constrained zero paths to be freely estimated. From notes: "Use LMtest to assess constraint that covariances between factors = 1." Also, with respect to respecification of Path, "Can remove nonsignificant parameters and test adequacy of resulting model" and "Use apriori LMtest to assess NS of omitting this parameter" I AM NOT SURE OF values suggesting that a parameter might added to the model to improve fit. I think that if the LM test for the parameters that you removed is nonsig, then you were correct to take them out. |
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Define/Describe Wald test (Wtest) and values suggesting that a parameter might be removed from the model without significantly decreasing fit.
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From Book:The Wald test is used for model trimming. A univariate Wald statistic approximates the amount by which the overall chi square statistic would increase if a particular freely estimated path were fixed to zero. Model trimming that is entirely empirically based would delete paths with wald W statistics that are not statistically dignificant.
From notes: Wald test |
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Define/Describe Hershberger's Replacement Rules
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Herschberger’s replacement rule applies to path models and to structural components of SR models.
HRR specifies path replacements that yield mathematically equivalent models. An equivalent model generates identical: |
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Define/Describe power ( to reject incorrect model, to dtect significant effects and parameter estimages).
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Power @ Model level—power to reject an
implausible model |
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How might SEM be used in the development and/or testing of a psychological test? Also discuss at least one limitation or problem with the use of SEM for assessing test items.
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CFA aspect of SEM can be used to assess the construct validity of a test. You ask: Can items group together in the way that is hypothesized? Does the factoral structure of the test reflect the way the subscales are.
Disadvantages: With maximum likelihood estimation, you'd assumed that the variables are normally distributed but when designing a test you might not want it to be normally distributed. In other words, CFA might not be the best method for doing item-level analysis. |
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Define/Describe Direct, indirect, and total effects in path analysis
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Each line with a single arrowhead represents a hypothesized DIRECT EFFECT of one variable on another. The arrowhead points to the presumed effect and the line originates from a presumed cause. Direct effects are also called paths, and statistical estimates of direct effects are path coefficients. Path coeficients control for correlations among multiple presumed causes of the same variable. (For example, the coefficient for the path Exercise-> Fitness controls for the correlation (db headed arrow) between exercise and hardiness.
Endogenous variables can be specified as direct causes of other endogenous variables. These dual roles are INDIRECT effects or mediator effects. INDIRECT EFFECTS involve one or more intervening variables presumed to "transmit" some of the causal effects of prior variables onto subsequent variables. For example: Exercise influences fitness, which in turn influences hardiness. INDIRECT EFFECTS are estimated statistically as the product of direct effects (standardized or unstandardized) that comprise them. Total effects in path = are the sum of all direct and indirect effects of one variable on another. |
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What is suggested by a statistically insignificant path coefficient or statistically insignificant direct, indirect, or total effect in path analysis?
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Statistically significant indirect effects but not direct effects demonstrates a possible mediation effect.
You can remove nonsignificant parameters in order to test the adequacy of resulting model (meaning I think that you can respecify). From notes: Path coeficients are similar to regression coeficients in that they control for correlations among multiple presumed causes. In unstandardized ssolution parameter estimates reflect the scales of the variables. Statistical tests are given for the unstandardized solution. In standardized solution the path coeficients can be compared directly. Nonsignificant path coeficients add little understanding to the data. For example, you may have a perfectly fitting (saturated model) with little relationship between variables. |
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What are rules of thumb suggested by Kline for interpreting the size of standardized path coefficients or of standardized effects?
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From notes:
Interpretation of direct effects (estimated from standardized path coeficients) varies with type of variable. General rules of thumb: greater than or equal to 0.10 is small greater than or equal to 0.30 is typical or medium greater than or equal to 0.50 is large. class 13 |
