Partial Least Squares (PLS) with Structural Equation Model (SEM)

Question 1

SEM is

Answer 1

Estimate models that seek to explain dependence (= predefined) rela’s among multiple var
- Series of rela’s can be explained simultaneously
- Nomological network (= part of construct validity)
- Fornell-Larcker test

Question 2

SEM two-language concept

Answer 2

To test rela’s.

• Theoretical language (abstract) > theoretical var
• Observational language > observable var (things we can measure)
  –> Match in terms of correspondence rules

Question 3

SEM steps

Answer 3

1. Examine measurement model (confirmatory FA because predefined rela’s)
2. Examine structural model (MRA)

Question 4

Why SEM?

Answer 4

• Model causal rela’s
  > Direct & indirect effects
  > Test full theory/whole model at once and adjust to contexts
• Accounts for measurement error
  > Accuracy & reliability
  > Fix errors to enhance trustworthiness of results
• Simple, visual models to explain/test

Question 5

PLS-SEM process

Answer 5

Define individual constructs –> specify model –> ensure requirements –> assess measurement model –> interpretation of measurement model –> assess structural model –> interpretation

Question 6

Distinguish types of SEM…

Answer 6

• Covariance based SEM
  > Starts by analyzing covariance matrix (= how var are together)
  > Confirmatory approach
  > Estimate model often done by Maximum Likelihood (ML), other options: WLS, ULS, GLS, ADF
• Variance based SEM
  > Starts by analyzing correlation matrix (= how strong are var rela’s)
  > Exploratory approach
  > Estimate model often done by PLS, other options: path analyzing using sum scores, GSCA

Question 7

Step 1: identify individual constructs

Answer 7

• Use existing scales if possible
• Best: multi-item measurement, but: single-item is ok for simple things

Question 8

Step 2: specify (measurement & structural) model

Answer 8

Structural:
- Which latent var do we include?
- Define rela’s (linear/nonlinear) between latent var
- Check for moderators, mediators, causal loops

Measurement: every latent var must have at least 1 indicators & vice versa
1. Reflective =
> latent var causes indicator
> arrow from oval to box
> indicators are usually correlated
> one can be dropped & keep meaning of construct
> related to CFA
> consumer research
2. Composite =
> indicators create constructs
> arrow from box to oval
> one dropped is change in meaning of construct
> indicators don’t have to be correlated
> weights are fixed or estimated (often using regression)
> problem: multicollinearity (PLS helps avoid it
> design/formative research

Question 9

Step 3: (assumptions &) requirements

Answer 9

• Sample size = highest # arrows pointing at 1 latent var *10 (preferrably >100)
• Data requirements: can be all (metric, categorical, and non-normale scale like skewed or bell-shaped)
  > So also incl categorical var with dummy var
• Model identification:
  > PLS needs context
  > Every construct needs to be related to at least 1 other construct & vice versa
  > Makes PLS more exploratory & good for theory development

Question 10

Step 4: assess measurement model [1]

Answer 10

Start with making sure indicators measure construct well.
> Only when reliable & valid, move on to structural model

Question 11

Step 4: assess measurement model [2]

Answer 11

Model fit:
- Does model match reality?
> Compare theoretical correlation matrix with real (observed) correlation matrix)
- Saturated model: diff small enough to be because of chance (so you want a nonsig p-value)
- SRMR <.08 to be of good fit

Question 12

Step 4: assess measurement model [3]

Answer 12

Reflective measurement:
- Reliability (all close to or >.7)
> Cronbach’s alpha but <.9/<.95 (>.6 for exploratory)
> Dillon-Goldstein’s rho
> Dijkstra-Henseler’s rho
- Indicator reliability
> Strong! = high loadings, ideally squared loadings >.4 (“item reliability”)
- Convergent validity
> AVE >.5 (unidimensionality, as well means 1 indicator = 1 construct)
- Discriminant validity
> HTMT <.85 (indicators belong to own constructs, not others)

Composite measurement:
- Expert judgement: do indicators make sense together?
- Indicator sig & relevance
- Nomological validity: behavior as expected in theory?
- External validity: correlation with similar reflective measures?

Question 13

Step 5: interpretation of measurement model

Answer 13

Iterative process

Question 14

Step 6: assess structural model [1]

Answer 14

Starts with saturated model fit
- Compare estimated correlations (model) with reality. If diff very small –> random error :)
> Use p<.05 –: if nonsig, model fits well

Question 15

Step 6: assess structural model [2]

Answer 15

Evaluate structural model (acceptable size depends on context):
- R2 (explained variance) (you get an R2 for every endogenous var)
- Path coefficients = arrows between constructs
> pos/neg?
- how strong is rela?

Question 16

Step 6: assess structural model [3]

Answer 16

F2 (effect sizes) = impact of specific var in model
- Helps identifying meaningfulness
- F2 > .35 = strong effect
F2 >.15 = moderate
F2 >.02 = weak

Q2 = predictive power (assessed by blindfolding), should be >.000

Question 17

Step 6: assess structural model [4]

Answer 17

Interconstruct correlation + indirect & total effects
= how constructs relate to eachother overall
& how var affect eachother through mediation

Question 18

Step 6: assess structural model [5]

Answer 18

Bootstrapping = getting sig
- Can’t use regular t-test because PLS doesn’t assume normale data
- Creates many small samples from original data and repeats
- Gives standard errors, avg estimates, confidence levels
> If t-level <-1.96 or >1.96 –> sig

Question 19

Key overview [indicator loadings]

Answer 19

_>.708 (HBAT)