G89 2247 Lecture 9 Thinking about an example Pitfalls in measurement models Pitfalls in model specification Item Parcel Issues G89 2247 Lecture 9 1 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 G89 2247 Lecture 9 2 Example of Model that cannot be fit using Exogenous Endogenous distinction E1 V1 E2 V2 E3 V3 E4 V4 E5 V5 E6 V6 Suppose that F1 is a baseline measure and F3 is the same measure at time 2 F1 the biases of E1 E2 and E3 may be reflected in E7 E8 E9 F2 D2 E7 V7 E8 V8 E9 V9 F3 D3 LISREL can also handle this by calling all variables endogenous G89 2247 Lecture 9 3 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 G89 2247 Lecture 9 4 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 G89 2247 Lecture 9 5 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 G89 2247 Lecture 9 6 Possible pathways L C C D C L C S D S D C D C D L S L G89 2247 Lecture 9 7 Possible Measurement Models Latent variables for Distress Support Coping Life Stress G89 2247 Lecture 9 8 Bollen and Lennox 1991 We can envision the relation between a construct and three manifest variables in two ways G89 2247 Lecture 9 9 Equivalent Models Some models that look very different have the same fit G89 2247 Lecture 9 10 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 2 151 173 G89 2247 Lecture 9 11 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 G89 2247 Lecture 9 12 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 G89 2247 Lecture 9 13 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 G89 2247 Lecture 9 14 Simple SEM Model Relating Depression to Outcome Y Parcel 1 Parcel 2 Depression Y Parcel 3 G89 2247 Lecture 9 15 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 G89 2247 Lecture 9 16 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 G89 2247 Lecture 9 17 Possible True Structures Second Order Factor Relation Suppose Y is related to second order factor 1 A1 1 1 A2 A3 1 B1 1 1 1 1 1 B2 B3 C1 C2 h h FA h g h h h h h h FB g F2 g a FC 1 C3 Y G89 2247 Lecture 9 18 Possible True Structures First Order Factor Unique Effects Graham and Tatterson 2000 considered this 1 A1 1 1 A2 A3 1 B1 1 1 1 1 1 B2 B3 C1 C2 C3 h h FA h g h h h h h h FB g F2 g b FC a b 1 b Y G89 2247 Lecture 9 19 Possible True Structures Item Unique Effects Mental health symptoms can have unique effects A1 A2 A3 B1 B2 B3 C1 C2 C3 h h FA h g h h h h h h FB g F2 g b FC a b 1 b Y G89 2247 Lecture 9 20 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 G89 2247 Lecture 9 21 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 G89 2247 Lecture 9 22 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 G89 2247 Lecture 9 23 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 …