Lecturer readiness: from CFA to a structural model

Check the factors before explaining adoption

Luo and Day surveyed 651 university lecturers in mainland China about generative-AI readiness. Their analysis used confirmatory factor analysis and covariance-based structural modelling, with further mediation and moderation analyses. The survey was cross-sectional and recruited through convenience networks.

In QuickPLS you will first fit a CFA for Support, Confidence and Intention, then create a separate structural model and request the indirect path through Confidence. This original continuous-data exercise follows the paper’s measurement-first approach without reproducing its full acceptance framework, scales or latent interactions. Good fit does not establish predictive accuracy.

Your study: support, teaching confidence and intention

Imagine 360 fictional lecturers considering a new teaching tool. Support is perceived institutional help, Confidence is perceived ability to use it in teaching, and Intention is a plan to adopt. Each is a common factor represented by three reflective continuous 1–7 teaching indicators.

A common factor is an underlying idea used to explain why its indicators vary together. First test that three-factor measurement model with the factors allowed to covary. In a separate structural model draw Support → Confidence, Confidence → Intention and Support → Intention.

The measurement and structural questions are related but distinct. The first asks whether the item relationships fit the proposed factors. The second puts a directed account on the factor relationships. Neither can establish that support was measured before confidence or that confidence caused adoption from a single cross-sectional table.

On a small screen, swipe the table sideways to see every column.

• Download the original lecturer-readiness exercise ↗
• Read the indicator and factor definitions ↗

Step 1. Import continuous teaching data and keep the original file

In a writable project choose File → Import Data… → Choose data file…. In Review & import select raw data, Header row 1, comma separation and Decimal convention Dot (1.25). Keep the nine teaching indicator columns Continuous. Choose Import dataset and confirm Dataset imported and verified with 360 cases.

All values are complete and point in the same direction. No reversal is needed. Keep case_id outside the measurement model. The continuous maximum-likelihood workflow taught here does not automatically provide an ordinal estimator for a real questionnaire with a few ordered categories.

Before fitting real data, check impossible codes, constant columns, duplicated items and missing values. Record how many cases remain. A solver can sometimes return numbers for a poor input or specification, so a completed calculation is only the start of assessment.

Step 2. Create three common factors with explicit markers

1. Create a measurement model

   Choose File → New Model…. Name it Lecturer readiness CFA, select the imported Dataset version, confirm 360 Cases and choose Create model. Leave the three directed research paths out for now.

2. Create and name the blocks

   Ctrl-select support1, support2 and support3 in Indicators, check 3 selected and choose Create construct. Select the construct and set Properties → Model → Name to Support. Repeat for Confidence and Intention using their matching columns.

3. Set the common-factor representation

   At the top of Properties set Inspector mode to Expert. For each selected construct open Parameter and choose Measurement model → Reflective. Under Scientific representation set Representation to Common factor.

4. Set each factor’s unit

   Choose Marker indicator support1 for Support, confidence1 for Confidence and intend1 for Intention. Confirm the common-factor message. The marker loading is fixed at 1 to establish the factor’s scale; do not type 1 into every loading.

5. Add the three factor covariances

   Use Connect to drag between each factor pair, then return to Select and click the relationship. In Properties → Parameter set Relationship type to Covariance. Under Relationship use choose Use → Model covariance and click Apply relationship use. Do this for Support ↔ Confidence, Support ↔ Intention and Confidence ↔ Intention. Save the CFA model.

Step 3. Fit the measurement-only model

Select Lecturer readiness CFA in Results before inspecting Model parameters and Standardized parameters. Check that support1, confidence1 and intend1 are the marker indicators and that the factor relationships belong to the measurement-only model.

1. Choose the CFA workflow

   Click Calculate… and select CB-SEM / CFA. Set Estimation workflow to Existing CFA / recursive SEM and Inference to Maximum-likelihood point estimates. Check that Model topology says Confirmatory factor analysis.

2. Calculate the selected model

   Confirm the dataset and complete-case preparation, review Readiness and choose Start calculation. Select this CFA result in Results and save it with the measurement model.

3. Read the parameter tables

   Use Search result outputs to find Model parameters and Standardized parameters. Read the fixed-marker rows, free loadings, factor relationships and residual variances. Then inspect Model fit and Diagnostics and warnings. Clear the search to see all output groups again.

Step 4. Read the scale, residuals and fit together

A marker fixed at 1 sets the factor’s unit. It does not mean the indicator measures Support or Confidence perfectly. A fixed parameter also does not have the ordinary estimated uncertainty of a free loading. Keep those roles distinct when filling a results table.

A residual variance is indicator variation left unexplained by its factor. A negative residual variance is an improper result to investigate, not a sign of exceptionally good measurement. Check factor correlations too: values that cannot form a valid relationship make the solution unusable, while extremely close factors can question whether the concepts are distinct.

Fit indices summarise mismatch between the model and the observed relationships. Chi-square and degrees of freedom describe the overall test under its assumptions. Approximate-fit indices and residuals provide other views. Inspect them together with the item content rather than declaring the model valid because one index looks favourable.

Step 5. Create a separate structural model without the CFA covariances

1. Recreate the same measurements

   Choose File → New Model… for the same dataset and name it Lecturer readiness Structural. Create the same three indicator blocks, Reflective measurement, Common factor representation and marker indicators used above.

2. Draw the proposed paths

   Use Connect to draw Support → Confidence, Confidence → Intention and Support → Intention. Return to Select and save. Support is the only factor without an incoming research path, so there is no pair of exogenous factors to connect by covariance. Do not copy all three CFA covariances into the structural model.

3. Choose structural estimation

   Open Calculate… → CB-SEM / CFA. Set Estimation workflow to Continuous-linear structural ML, Moment structure to Covariances and Inference to Maximum-likelihood point estimates. For practice use Maximum iterations per stage 1000 and Convergence tolerance 0.0000001. Under Numerical solver choose Solver → Improved convergence.

4. Check completion and the model results

   Review Readiness and choose Start calculation. If a protected project copy is returned, continue there while retaining the original. In Results select Lecturer readiness Structural. Check convergence and Diagnostics and warnings before reading Model parameters, Standardized parameters and Model fit.

   What you should see: The selected result belongs to the structural model, with the three research paths rather than the CFA’s factor covariances.

Check the factor models for these 360 cases

Use continuous maximum likelihood with the first indicator loading fixed to 1 for each factor. The CFA allows every factor pair to covary. The structural model retains only the paths and exogenous-factor covariances listed in this lesson. No indicator residual covariance is added.

The CFA and structural model have the same fit to numerical precision. The three-path structural model re-expresses the same three-factor covariance structure. That does not establish that Support came before Confidence or that Confidence caused Intention.

About these answers: Comparison answers calculated in lavaan 0.7.3, with independent checks of covariances and standardised estimates.

On a small screen, swipe the table sideways to see every column.

• Download the exact setup, unrounded answers and reference script ↗

Read the structural estimates on the right scale

The raw coefficient uses the marker-defined factor unit. The standardised coefficient uses standard-deviation units. The displayed interval belongs to the raw estimate; do not attach it to the standardised value.

About these answers: External ML point estimates. The intervals below are normal-theory Wald intervals, not the case-bootstrap intervals requested later in the app lesson.

On a small screen, swipe the table sideways to see every column.

Good fit does not select the causal order

This structural model includes all three forward relationships among three factors. A flexible directed model can account for the same factor-covariance pattern as the measurement model under compatible assumptions. Similar fit therefore would not establish that Support caused Confidence and then Intention.

The numerical solver searches for parameter values under the specification. Convergence indicates that its stopping conditions were met. It does not verify the study’s time order, sampling design or omitted influences. Check that the estimates are mathematically usable before discussing whether the scientific explanation is credible.

An unstandardized path uses the marker-defined factor units. A standardized path uses the scaling named in the output. Keep the coefficient and interval on the same scale. Never attach an original-unit interval to a standardized coefficient just because the rows are close together in a report.

Step 6. Add matching structural uncertainty

Return to Calculate… → CB-SEM / CFA for the structural model. Keep Estimation workflow → Continuous-linear structural ML and Moment structure → Covariances. Set Inference to Case-resampling bootstrap. Under Bootstrap choose Bootstrap samples 1000, Confidence level (%) 95, Interval method Percentile (Type 7), Alternative Two-sided and Seed 202611087. These are practice choices in the ordinary Calculate interface.

For the indirect route choose Structural effects → Effects with bootstrap inference. Open Requested effects and path limit, choose Add requested effect and set Effect type to Specific indirect path. Select Support → Confidence under Path step 1 and Confidence → Intention under Path step 2. Keep the complete model, including the direct Support → Intention path.

Start calculation and inspect the original fit, usable refits and failures before reading intervals. The Improved convergence point-solver choice does not describe every bootstrap procedure. Keep the actual inference settings with each effect. An unavailable effect interval needs its recorded reason, not a substituted interval from a different quantity.

Resolve an improper solution before explaining a relationship

On a small screen, swipe the table sideways to see every column.

Revise an item relationship for a reason beyond fit

If residuals suggest that two items share something beyond their factor, inspect their wording and administration. A justified shared wording effect might motivate a separate revised model. Adding residual covariances simply in order of the largest suggested improvement turns the exercise into an exploratory search.

Keep the original CFA and structural specifications. Explain what a revision changes about the measurement or research question, and use suitable compatible comparisons where appropriate. More iterations cannot identify a model that lacks enough information, and deleting a difficult indicator can narrow the construct.

A real lecturer study also needs a defensible recruitment and response account. Convenience respondents are not made nationally representative by a well-fitting model. The current lesson isolates calculation and interpretation using independent invented cases; it cannot supply a real study’s sampling argument.

Report measurement, structure and uncertainty as separate steps

Methods outline: We first fitted a three-factor continuous maximum-likelihood CFA with [markers] and all three factor covariances. We then fitted a separate structural model with Support → Confidence, Confidence → Intention and Support → Intention, retaining the same measurement and factor scales. We checked convergence, usable parameter values, fit and residuals. Structural uncertainty used [actual case-bootstrap settings and usable counts].

Results outline: The measurement model showed [loadings, factor relationships, residual and fit findings]. The structural paths were [estimates on a named scale with matching intervals]. The Support → Confidence → Intention association was [estimate and interval]. These results describe the specified factor relationships and do not prove causal ordering or out-of-sample predictive accuracy.

Explain the model comparison

We fitted the stated CFA and structural model to 360 synthetic teaching cases using continuous maximum likelihood and first-indicator markers. We kept the CFA measurement covariances separate from the structural specification.

Report fit and measurement evidence before the paths. If you use the reference intervals here, call them normal-theory Wald intervals. The lesson’s app bootstrap is a separate procedure with its own resampling count, failures and intervals.

Explain why a good-fitting model still needs a research argument

• Show the Common factor and Marker indicator settings for each construct.
• Distinguish a factor covariance from a directed research path.
• Explain why a fixed marker of 1 does not mean perfect measurement.
• Identify an improper result that fit indices cannot excuse.
• Check the actual Support → Confidence → Intention product using the saved full-precision raw estimates. If you calculate its bootstrap interval, report that named product interval; do not borrow either component path’s interval. Keep the hypothetical 0.21 example separate.
• Keep the CFA, structural point result and matching bootstrap as separate saved calculations.