G Lecture 91 Thinking about an example Pitfalls in measurement models Pitfalls in model specification Item Parcel Issues

G Lecture 92 Review of SEM Notation LISREL’s distinction between exogenous and endogenous variables simplifies the computational expressions.    Y  y   X=  x  EQS and AMOS use an approach that does not make this distinction  Essentially, all variables are potentially endogenous  This allows for a wider class of models to be considered, especially with regard to correlated residuals.

G Lecture 93 Example of Model that cannot be fit using Exogenous/Endogenous distinction Suppose that F1 is a baseline measure and F3 is the same measure at time 2.  the biases of E1, E2 and E3 may be reflected in E7, E8, E9. LISREL can also handle this by calling all variables endogenous V1 V2 V3 V4 V5 V6 V7 V8 V9 F1 F2 F3 E1 E9 E8 E7 E6 E4 E3 E2 D3 D2 E5

G Lecture 94 How would we model this example? Stressful life events(L) both result from and lead to mental dysfunction(D), but coping strategies(C) can reduce the impact of the stressful events, as can support (S) Stressful Events, distress, coping, support are typically measured by self-report, which may introduce error Panel data is sometimes helpful to study the processes

G Lecture 95 Suppose we have these measures at three points in time L: Life events  School hassles (count per week)  Family conflicts (count per week)  Urban events (thefts, traffic jams, etc) D: Distress  Anxiety  Depression  Anger  Low self esteem

G Lecture 96 Suppose we have these measures at three points in time (continued) C: Coping  Denial actions  Distraction actions  Problem-focused actions S: Support  Perceived support from confident Hugs and kisses, practical help  Confidant's report of support Hugs and kisses, practical help

G Lecture 97 Possible pathways L => C C (-)=>D C (-)=> L C => S D => S D (-)=> C D =>C D => L S => L

G Lecture 98 Possible Measurement Models Latent variables for  Distress?  Support?  Coping?  Life Stress?

G Lecture 99 Bollen and Lennox(1991) We can envision the relation between a construct and three manifest variables in two ways:

G Lecture 910 Equivalent Models Some models that look very different have the same fit

G Lecture 911 Issues in Defining Measurement Models Latent variables are used to correct for error through multiple indicators  Sometimes multiple indicators do not exist  Some researchers suggest making up quasi multiple indicators by creating “parcels” of items The proper use of parcels is controversial  E.g. Little, Cunningham, Shahar, Widaman (2002) To parcel of not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling 9(2),

G Lecture 912 Example: CES-Depression "Scale" DURING THE PAST WEEK  I felt depressed.  I felt that I could not shake off the blues even with help from my family or friends.  I felt sad.  I could not get going.  My sleep was restless.  I felt that everything I did was an effort.  I felt that people dislike me.  I thought my life had been a failure.  People were unfriendly.

G Lecture 913 Conventional Use of Scales Such as CES-D Items have 0-4 response categories Factor structure is generally ignored Items are summed without weights into a single scale score Alpha coefficient of.8 to.9 generally underestimates true reliability Test retest reliability often high despite explicit time frame

G Lecture 914 Relation of Outcome Y and CES-D Accounting for Measurement Error Suppose Y is measure of functioning in workplace SEM approach can be recommended for CES-D, BUT  Studies usually do not have multiple indicators of depression other than items  Sample sizes usually do not allow item-level analyses Kishton and Widaman (1994) laid out alternative approaches to forming parcels.  Factor-based unidimensional parcels (FBP)  Domain Representative parcels (DRP)

G Lecture 915 Simple SEM Model Relating Depression to Outcome, Y Y Depression Parcel 1 Parcel 2 Parcel 3

G Lecture 916 Factor-based Unidimensional Parcels Form parcels with items that relate to specific subdomains of scale E.G., FBP1=A1+A2+A3 A1: I felt depressed. A2: I felt that I could not shake off the blues even with help from my family or friends. A3: I felt sad.

G Lecture 917 Domain Representative Parcels Form parcels with items that span the subdomains of item set E.G., DRP1=A1+B1+C1 A1: I felt depressed. B1: I could not get going. C1: I felt that people dislike me. Parcels are designed to be close to parallel measures

G Lecture 918 Possible "True" Structures: Second Order Factor Relation Suppose Y is related to second order factor h h h h h h h h h FA FB FC A1 A2 A3 B1 B2 B3 C1 C2 C3 1 a g g g F2 Y

G Lecture 919 Possible "True" Structures: First Order Factor Unique Effects Graham and Tatterson (2000) considered this h h h h h h h h h FA FB FC A1 A2 A3 B1 B2 B3 C1 C2 C3 1 a g g g F2 Y b b b

G Lecture 920 Possible "True" Structures: Item Unique Effects Mental health symptoms can have unique effects h h h h h h h h h FA FB FC A1 A2 A3 B1 B2 B3 C1 C2 C3 1 a g g g F2 Y b b b

G Lecture 921 Exploration of Parcel Strategies for Different Assumed Structures Parcel models are generally mispecified relative to assumed model  Exception is FBP parcel model for Second Order Factor relation What is direction and magnitude of bias?  Look at R-Square and parameter estimates Compare to simple sum of CESD items

G Lecture 922 Simulated Results Assuming Second Order Factor Relation Parameters in structure considered  First order factor loadings.7  Second order factor loadings.7  Structural path.7  True R square.50 R square for simple sum of nine items: 0.31 R square for FBP parcel model: 0.50 R square for DRP parcel model: 0.37

G Lecture 923 Simulated Results Assuming Second Order Factor Plus Unique First Order Factor Effects Parameters in structure considered  First order factor loadings.7  Second order factor loadings.7  Structural paths.55 SOF,.20 unique FOF  True R square.49 R square for simple sum of nine items: 0.31 R square for FBP parcel model: 0.61 R square for DRP parcel model: 0.45

G Lecture 924 Simulated Results Assuming Second Order Factor Plus Unique Effects for Items Parameters in structure considered  First order factor loadings.7  Second order factor loadings.7  Structural paths.45 SOF,.10 unique item  True R square.54 R square for simple sum of nine items: 0.46 R square for FBP parcel model: 0.71 R square for DRP parcel model: 0.54

G Lecture 925 Conclusion If one has confidence that a second order factor accounts for the relation between scales like the CESD and outcomes  Factor Based parcels are ideal  Domain Representative parcels do better than sum score If the relation between an outcome and a heterogeneous item set involves first order unique factors or unique item effects  The FBP parcels can be misleading  Domain Representative parcels do better than sum score

G Lecture 926 Comment on Bias of FBP The correlations of Y to the FBP1, FBP2 and FBP3 are larger than what is explained by the original conceptual model.  Cohen, Cohen, Teresi, Marchi, Velez (1990) Y becomes the dominant indicator of the latent variable. Y Depression Parcel 1 Parcel 2 Parcel 3 Y