Structural Equation Modeling Exam I Study Guide Q

Front 1

Determinant of input matrix

Back 1

Determinant = generalized variance
of the matrix to be analyzed. If 0, some
calculations cannot be done. If close to 0
suggests multicollinearity and unreliability
of estimates.

Front 2

Lagrange Multiplier test (LMT or LMtest)

Back 2

The Lagrange Multiplier test (LMT or LMtest) tells you how much model fit would improve if fixed parameteres are freed. (For example, if an indicator were allowed to load on another factor, if errors were allowed to correlate). The LMT can also be used to test equality constraints. The LMT may specify particular sets of parameters to consider, using matrix notation.

Front 3

Unit variance identification

Back 3

scale
of latent variable set by fixing its
variance to 1 (standardized model).

Front 4

Unit loading identification

Back 4

scale
of latent variable set by fixing path for
one of its indicators to 1.

Front 5

Multidimensional measurement

Back 5

multidimensional measurement = An indicator has loadings on more than
1 factor, or some error terms covary with each
other
-It can be more difficult to establish identification with a multidimensional measurement model. You may have problems if both correlated errors and loadings of indicators on multiple factors are specified.

Front 6

unidimensional measurement

Back 6

-Each indicator depends on just 1 factor
-Error terms are independent (none of the errors are correlated).
-Can be easier to achieve identification with a unidimensional measurement model than with a multidimensional measurement model.
-In terms of the establishment of identification in a unidimensional measurement model:
-If you have a 1 factor CFA model you need at least 3 indicators
-If you have a 2 or more factors in your CFA model you need at least two indicators per factor (but more likely to have estimation problems if <3)

Front 7

2nd order CFA model

Back 7

In a 2nd order CFA model, (Hierarchical), A
higher order factor, without direct
indicators, is presumed to cause 1st
order factors. First order factors
are endogenous.
(see pg 3 of class 6 for diagram)

Front 8

1st order CFA model

Back 8

In a 1st order CFA model, the factors are exogenous variables with observed variables as indicators.
see diagram on pg 3 of class 6

Front 9

Multicolinearity

Back 9

Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated.

You are trying to avoid excessive multicolinearity when screening a raw data file.

If the determinant of the input matrix is close to 0, this suggests MULTICOLINEARITY and unreliability of estimates.

Front 10

Ill scaled variables

Back 10

Ill scaled variables are variables where the ratio of largest to smallest variance > 10.

You are trying to avoid ill scalled variables when screening a raw data file.

Front 11

Multivariate outlier

Back 11

Not totally sure that this is right, STILL NEED TO LOOK IN TEXT TO BE SURE:

The basis for multivariate outlier detection is the Mahalanobis distance. The standard method
for multivariate outlier detection is robust estimation of the parameters in the Mahalanobis distance
and the comparison with a critical value of the Chi squared distribution. I think that visualizing multivariate outliers of spatial data is possible.

Outliers (> ± 3.00 SDs)

Front 12

univariate outlier

Back 12

Not totally sure that this is right, STILL NEED TO LOOK IN TEXT TO BE SURE:

Many methods have been proposed for univariate outlier detection. They are based on (robust) estimation of location and scatter, or on quantiles of the data.

Outliers (> ± 3.00 SDs)

Front 13

Write /EQUATIONS paragraph of EQS output.

Back 13

The EQUATIONS paragraph defines every regression path in the model, Identifies fixed and free (*) parameters, and should contain as many equations as dependent (endogenous) variables in
model.

See paint

Front 14

Write /Variances paragraph of EQS output.

Back 14

Not completely sure CHECK BK OR ASK TA

/Variances identifies variances associated with independent variables as either fixed or free.

To estimate variance of A:
/Variances
A=*

Front 15

Write /COVARIANCES paragraph of EQS output

Back 15

NOT SURE - CHECK BK OR ASK TA

/COVARIANCES specifies any covariances to be estimated between independent or exogenous variables

/COVARIANCES
F1-F3=*
This is telling you to estimage all the possible covariances between latent variables F1, F2, and F3.

Front 16

What does it mean if an individual parameter in the model is not significant?

Back 16

Nonsignificant parameters are of no
interest in model and should be
considered for deletion (or can indicate
small sample size).

Front 17

What does it mean if goodness of fit statistics suggest that a model has good fit?

Back 17

The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question.

(Therefore,if a model has good fit:
-the observed values closely resemble those expected by the model

-The Chi Square (a measure of goodness of fit) is non significant (meaning that all residuals are not zero, having the model is better than having no model at all)

-RMSEA<.05 suggests good fit, implying that the model fits the population's covariance matrix reasonably well.

Absolute Fit index will be >0.90 for good fit.

Comparative fit index >0.90 means good fit?, suggests that the model is different than the null model when adjusting for sample size?

(Frequency centers around 0 and is fairly symmetrically
distributed if good fit)?.

Front 18

Why does Byrne recommend using the CFI instead of the NFI or the GFI? Why does she suggest also reporting the RMSEA?

Back 18

Byrne recommends the Comparative Fit Index instead of the Normed Fit index because the NFI Underestimates fit in small samples, while the
Comparative Fit Index (CFI)—
adjusts NFI for sample size.
Both range from 0-1.00

The comparative fit index is derived from comparison to
Independence model.
Cut-offs: >.90 and more recently >.95

Byrne thinks that you should use the CFI instead of the Goodness of Fit Index (which is an absolute fit index) because the GFI has been
criticized for insensitivity of misspecified models and
can be strongly influenced by sample size.

Byrne recommends reporting the RMSEA because confidence intervals can be affected by both sample size and model complexity (in a small sample, RMSEA will underestimate fit).

Front 19

What indicators does Kline recommend for assessing goodness of fit? What are the target values?

Back 19

???(e.g., Chi Square model, should be NS, but highly sensitive to sample size; Comparative Fit Index (CFI; Bentler) > .95; Root Mean Square Error of Approximation (RMSEA) and confidence interval, should ideally be <.05, > .10 poor fit).

Front 20

What can account for empirical under-identification in a theoretically identified model?

Back 20

A statistical model is ‘identified’ if the known information available implies that there is one best value for each parameter in the model whose value is not known. For example,the following is not identified



x +2y=7



since there are an infinite number of pairs of x and y values which satisfy the above equation. However, if a further equation is also specified



3x-y=7



there is only one pair of values which satisfy the two simultaneous equations, and the system is ‘identified’.

Under-identification refers to a failure of the model, independent of the observed data. Unfortunately, even if a model is identified, particular data being used with the model may still result in ‘empirical under-identification’

Empirical Underidentification
Kenny (1979) introduced this term for situations where a model should be identified based on its structure, but it is not identified based on the sample data being analyzed. For example, a measurement model with two correlated constructs and two congeneric measures loading on each construct should be identified, under the "Two Indicator Rule." But suppose that, in a given sample of data, the correlation between the constructs is equal to 0. Then, in that sample, the model would not be identified. As Kenny (1979) noted, the threat of "empirical underidentification" means that researchers must always be alert for signs of identification problems, even when a model is nominally identified based on its structure

Front 21

What are the two techniques that can be used to set the scale of the latent variables in CFA?

Back 21

ULI (unit loading identification)—scale
of latent variable set by fixing path for
one of its indicators to 1.

UVI (unit variance identification)—scale
of latent variable set by fixing its
variance to 1 (standardized model).

CFA model—hypothesizes that
observed variables are valid indicators
of latent variables & any associations
between the latent variables

Front 22

define/describe Path Analysis - Structural model

Back 22

Path model—hypothesizes relationships between
observed variables, no latent variables included

I DON'T KNOW IF THIS IS ALL OF THE INFO ABOUT THIS.

Front 23

Describe the six basic steps of SEM described by Kline?

Back 23

1. Determine model (structural models can include CFA, Path, SR)

2. Determine whether or not the model is identified:
-can you obtain unique estimates of parameters
- do you have enough information to
estimate model)
- At minimum number of observations
(values in covariance matrix) must
exceed parameters to be estimated

3. Select measures for variables
included in the model:
- Look at previous literature to select
reliable and valid measures
- Be sure that you have enough and
representative indicators for each
latent variable
- Collect, prepare, and screen the data,
adjusting indicators and model if
necessary

4. Use a computer program (e.g.,
EQS, LISREL, AMOS) to estimate
the model
- Evaluate fit of the model
- If the model fits:
Interpret parameter estimates (e.g.,paths between variables)
Consider equivalent models

5. If necessary (e.g., model fit is not optimal), respecify the model
- Respecification is guided by theory,
previous research, and statistical
output from the program
- Test the revised model
- Continue this step as long as theory, research, and statistics justify (It may
be necessary to make a number of incremental revisions).

6. Accurately and completely describe the analyses
and results in written reports. For example--
- Description of the sample
- Handling of data (any violations of assumptions,
any transformations, missing data, etc.)
- Complete description of model(s) tested (e.g.,
what indicators were used for each latent variable)
- Parameter estimates
- Matrix estimated
- Other descriptive data (means, SD’s)
- Methods of assessing model fit and effects

Front 24

What are indications that a set of observed variables has excessive multicollinearity?

Back 24

!!!DON'T THINK THAT THIS IS RIGHT- NEED TO LOOK UP!!!

If the determinant of the input matrix is close to zero, then multicolinearity may be present

Multicollinearity refers to excessive correlation of the predictor variables. When correlation is excessive (some use the rule of thumb of r > /90), standard errors of the b and beta coefficients become large, making it difficult or impossible to assess the relative importance of the predictor variables

Front 25

When would analysis of standardized variables be particularly inappropriate?

Back 25

Analysis of standardized variables
inappropriate if

Front 26

What are the minimum requirements for identification of a model? (3 requirements)

Back 26

1. Df greater than or equal to 0
2. You have at least as many OBSERVATIONS as free model parameters. Here's how to calc # of observations:
Number of observations = (number of observed variables)* (number of observed variables +1)/2 AKA Number of observations = v*(v+1)/2
3. Each latent variable is ASSIGNED A SCALE by either fixing loading of a reference on an observed variable or by fixing the variance of a latent variable.

Front 27

What data are required to generate a covariance matrix?

Back 27

1.. The covariance matrix accounts for both relationships between variables (correlations) and their variance (standard deviations).
2. You can generate a covariance matrix for analysis from raw data or from correlation matrix and standard deviations.

The covariance matrix uses nonstandardized variables.

Front 28

What is the basic matrix analyzed in SEM?

Back 28

I think it is covariance matrix.

Front 29

In what ways is SEM an a priori technique and in what ways is it exploratory?

Back 29

It is a priori in the sense that it is a confirmatory technique in which you must specify a model to conduct analyses. Model specification is guided by domain knowledge, theory, and previous studies.

It also has exploratory features...NOT SURE WHAT THEY ARE

Front 30

What are the three types of applications of SEM described by Joreskog?

Back 30

1. Strictly confirmatory (that is, the model is tested and is either accepted or rejected).
2. Comparison of alternative models
3. Model generating, in which respecification of an initial model is based on statistical results and theory. This is the most common application of SEM. If you test an initial model and the fit isn't good, you use the results to incrementally alter the model to improve fit. Only alter the model in ways that make sense theoretically

Front 31

What is the purpose of SEM or what type of hypothesis does it test?

Back 31

Tests confirmatory hypotheses for which you have specified a model?? I'm not sure

Front 32

Define/Describe Kurtosis—positive and negative

Back 32

A platykurtic distribution has a flatter peak.
(- Kurtosis)

A leptokurtic distribution has a higher peak. (+ kurtosis)

Kurtosis = degree of elevation and spread of curve
Kurtosis cut off = + or - 8 to 20

Front 33

Define/Describe Skew (pos and neg)

Back 33

pos skew - most scores below the mean (tail on right)

negative skew - most scores are above the mean. (tail on left)

Skew means that the distribution is asymetrical about the mean.

Front 34

Define/Describe Interaction efffects

Back 34

Typical SEM procedures estimate linear associations, though it may be possible to represent curvilinear or interaction effects.

Special variables (like product terms) can be used to represent curvilinear or interaction effects

Interaction (aka moderation) = The relation
between x and y varies as a result
of a third (moderating) variable

See diagram

Front 35

Define/Describe Recursive model

Back 35

A recursive model specifies the direction of cause from one direction only (i.e., the direction of causality only goes one way)

See diagram

Front 36

Define/Describe Nonrecursive model

Back 36

A non-recursive model allows for reciprocal or feedback effects but makes it more difficult to achieve identification.

See diagram

Front 37

Define/Describe number of observations.

Back 37

Number of observations = (number of observed variables)* (number of observed variables +1)/2 AKA Number of observations = v*(v+1)/2

Front 38

Define/Describe Identified model

Back 38

An identified model is one in which it is theoretically possible to derive a unique estimate of each paramenter.
(NOT something like y+x=10, in which you could have more than one value of x or y)

Front 39

Define/Describe E

Back 39

E= unique variance associated with an observed variable.

I think E also refers to error:
Errors are residuals associated with observed variables (e.g., measurement error, unique variance). Errors are represented in the path diagram as arrows that go from the latent variables to the observed construct (i.e., the tip of the arrow points to observed construct).

Front 40

Define/Describe D

Back 40

D = disturbance

Disturbance is the residual or error in the prediction of a latent variable.Disturbance terms pertain to ENDOGENOUS latent variables only. Distrubance terms are represented in a path diagram by a sideways slanting arrow.

Front 41

Define/Describe the IVs in SEM

Back 41

Exogenous variables = IVs

Exogneous variables (IVs) "cause" variance in endogenous variables

Front 42

Define/Describe DVs in SEM

Back 42

DVs = endogenous variables

Endogenous variables (DVs) are influenced by exogenous variables in the model

Front 43

Define/Describe SR.

Back 43

SR = Structural Regression

SR is one of the different models that can be tested (that is, you can use CFA, path, or SR).

If you were to do Structural Regression, then We could analyze predictive relationships between latent
variables.

Front 44

Define/Describe Path Analysis

Back 44

A path analysis is one type of the 3 possible structural models that can be tested in SEM (the others are CFA and SR).

The Path model hypothesizes relationships between
observed variables, no latent variables included

Front 45

Define/Describe CFA.

Back 45

CFA is one of the structural models that can be tested in SEM (apart from Path and SR).

In CFA, it is hypothesized that
observed variables are valid indicators of latent variables any associations
between the latent variables

Front 46

Compare/Contrast the 3 types of structural models that can be tested in SEM.

Back 46

CFA = hypothesizes that
observed variables are valid indicators
of latent variables any associations
between the latent variables

Path =hypothesizes relationships between
observed variables, no latent variables included

SR = analyze
predictive relationships between latent
variables, instead of observed variables

Front 47

Define/Describe F.

Back 47

F = latent variables

Latent variables are hypothetical constructs that are assumed to "cause" variance in observed variance. Latent variables are represented by ovals.

Front 48

Define/Describe V

Back 48

V = observed variables

Observed variables are indicators of unobserved latent variables Represented by squares

I think that an observed variable can also be referred to as an indicator.