Overview
Stability Analysis evaluates how a class of related stimuli controls behavior over time and under varying conditions. Essentially, it measures whether the relational responses among the stimuli remain robust and stable over time and across contexts—an essential aspect in both Precision Teaching and behavioral interventions.
Key Components of Stability Analysis
Response Consistency (Aim rate). Assess whether each member of the relational class consistently evokes the target behavior (e.g., a specific response such as R1) across repeated measurement sessions. In a stable system, performance should remain relatively constant even with extended exposure.
Resistance to Disruption (Stability). Evaluate how well the relational responding withstands changes in conditions, such as distractions, environmental variations, or contextual shifts. A stable relational coordination class will show minimal degradation in performance under these perturbations.
Maintenance Across Time (Retention and Endurance). Stability is shown if the target behavior persists over time, particularly when there is no immediate reinforcement. This involves checking for retention (accuracy over time) and endurance (sustained performance over longer sessions or repeated trials).
Generalization (Application/Generalization). Confirm that the established relational responses apply to new or similar stimuli not directly trained. High stability suggests that the relational coordination extends beyond the specific instances met during training.
Methodology and Measurements for Stability Analysis
Rate Counts. Measure the responses per minute rate for each stimulus in the 5-member class in evoking the target behavior (see/say, hear/say, read/say, see/write, etc.)
Probes Across Sessions. Conduct multiple probes over several days to measure performance consistency.
Perturbation Tests. Stability - introduce controlled distractions or context changes during some probes to assess resistance to disruption.
Metrics and Analysis
Eigenvalue Calculation. Compute the eigenvalue for the class (average performance across all members). A high eigenvalue suggests strong relational cohesion. In control theory, eigenvalues of a system's (here, the relational class) state matrix help determine stability. For instance, if all eigenvalues have negative real parts, the system will return to equilibrium after a disturbance; if any eigenvalue has a positive real part, it indicates an instability that could lead to uncontrolled behavior.
Variance Analysis. Examine the variability in responses across the stimuli. Low variance indicates a stable, well-coordinated relational class.
Trend Analysis. Use graphical tools (line charts or control charts) to visually inspect performance trends across sessions. Stability is indicated by minimal drift or sudden drops in performance.
Interpretation and Implications
High Stability. If the analysis shows minimal variance, high eigenvalues, and consistent performance across varied conditions, it indicates that the relational coordination class effectively controls behavior. This stability supports the notion that the relational responses are robust, reliable, and likely to generalize in new contexts.
Low Stability. Conversely, if significant fluctuations occur—especially when minor perturbations are introduced—it may suggest that the relational class is fragile. In such cases, further training or reinforcement might be necessary to bolster the stability and reliability of the target behavior.
Behavioral Control. In stable systems, the behavior is not only consistently evoked but also shows resistance to extinction and external distractions. This control is crucial for practical applications such as skill generalization, transformation of function, and adaptive behavior under real-world conditions.
Discussion
Applying stability analysis to a 5-member relational coordination class involves a thorough examination of response consistency, resistance to disruptions, and long-term retention. By using metrics such as eigenvalues and variance analysis, along with systematic probing under varied conditions, one can find the degree to which the relational class controls behavior. High stability indicates a robust, well-coordinated relational system, essential for effective and generalized behavioral interventions.