1. Separate Constructs for Objective and Subjective Performance

Treat objective performance and subjective performance as separate but related latent variables.

Model firm performance as a higher-order latent variable (HOC) with two dimensions:

Objective Performance (indicators based on your categorical variable).

Subjective Performance (indicators from your Likert scale).

This approach captures the multidimensional nature of firm performance without requiring merging or rescaling.

2. Handling Objective Performance (Categorical Data)

Categorical data (e.g., performance categories like 0–20%, 21–40%) can be treated as indicators of a latent construct.

If you want to simplify for analysis, midpoints can be used to represent the categories numerically (e.g., 0–20% = 0.10, 21–40% = 0.30).

Caution: This assumes the intervals are meaningful and equidistant. While it enables ordinal representation, it may oversimplify or misrepresent nuanced relationships.

Alternatively, use dummy variables to represent categories if there’s no inherent order.

3. Combining with Subjective Performance (Ordinal Data)

For subjective performance measured on a 7-point Likert scale:

Directly use the Likert-scale responses as reflective indicators.

If the scale is treated as interval (common in PLS-SEM), ensure consistency in interpretation across the model.

4. Modeling a Higher-Order Construct

Use the two-stage approach or repeated indicator approach to model firm performance as a higher-order construct in SmartPLS:

First-order latent variables: Objective and subjective performance.

Second-order latent variable: Firm performance, capturing the overall performance construct.

5. Statistical Considerations

Converting Objective Performance to Midpoints:

Pros: Simplifies analysis and allows integration with ordinal subjective measures.

Cons: Assumes equidistance between categories, which may not always reflect reality.

Use this approach only if the categories are genuinely ordinal and approximately equidistant.

Measurement Model Evaluation:

Ensure each latent construct (Objective and Subjective Performance) has adequate reliability (Cronbach’s Alpha, Composite Reliability) and validity (Convergent and Discriminant Validity).

PLS Algorithm:

PLS-SEM is robust to non-normal data and differences in scale, making it well-suited for your case.

6. Practical Steps in SmartPLS

Create Latent Variables: Define Objective Performance and Subjective Performance as separate latent variables with their respective indicators.

Define Firm Performance: Set up Firm Performance as a higher-order latent variable using either:

Repeated Indicator Approach: Assign all indicators of Objective and Subjective Performance to Firm Performance.

Two-Stage Approach: Aggregate first-order latent variables into the second-order latent variable.

Assess Model Fit: Ensure that the model structure, relationships, and results make theoretical and practical sense.

Recommendation

If you choose to use midpoints, document and justify the assumption of equidistance explicitly. If you’re uncertain, the higher-order modeling approach with categorical data as separate indicators is safer and preserves the integrity of your scales.

If your objective indicator was originally measured on a continuous scale (zero to 100%), you are loosing information unnecessarily when you reduce it to categories.

Any dependent variable can be added to the problem within the model and its effect measured, then it is either ignored or taken into account.@