On the importance of specifying explicit response functions in preference, emotion and behavior measurement
|
Yvonnick Noel
LP3C, University Rennes 2, Brittany, France
17th Sensometrics Conference, Paris, June 4th, 2024
|
|
http://yvonnick.noel.free.fr/papiers/respfunc
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
The Semantic Differential approach
- In his seminal 1952 paper "The Nature and Measurement of Meaning." Osgood developed a method to quantify the subjective meanings that people associate with various concepts or objects.
- Respondents are presented with a series of bipolar adjective pairs (e.g., happy-sad, strong-weak) and asked to rate a concept or object on these scales.
- For example, the SD has been used to measure the subjective perception of, and affective reactions to, marketing communication (Kriyantono, 2017), political candidates (Franks & Scherr, 2014), alcoholic beverages (Marinelli et al., 2014) and websites (Van Der Heijden & Verhagen, 2004).
A stable structure
- From factor analyses on ratings of evaluation adjectives on various objects and concepts, Osgood found three recurrent factors: Evaluation (good-bad), activity (active-passive) and potency (strong-weak).
- Interestingly, a very similar three factor solution is regularly found (Mehrabian & Russell, 1974) in the analysis of emotion, under the names: Valence (positive vs. negative affect), Arousal (Active vs. Passive) and Dominance (Control vs. Helplessness).
- It would not be difficult to reformulate current (five-factor) models of personality around three main components (Noel, 2015): Emotional valence (Neuroticism vs. Extraversion), Cognitive Arousal (Openness to Experience vs. Conservatism) and Control (Conscientiousness vs. Impulsivity).
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
An illustrative study
- 157 subjects (125 females and 32 males) were recruited for an emotion induction experiment (Noel, 2024, unpublished). Subjects were randomly assigned to one of four induction conditions: i) Neutral, ii) Anger, iii) Joy and iv) Sadness.
- The standardized Mayer et al. (1995) induction protocol was used, were subjects had to read a set of eight inducing sentences, while listening to an appropriate type of music.
- Subjects had to rate their emotional state twice, before and after the induction phase on the same set of 40 adjectives.
PCA of initial states (unrotated)
PCA of initial states (VARIMAX rotation)
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
The Linear Response Model
- Key point: Measuring a psychological state (or preference or ability) implies a (potentially implicit or ignored) hypothesis on a response function relating the observed response to the latent state.
- Otherwise stated: Measuring is modelling.
- The simpler model is probably the Linear Response
Model (Mellenberg, 1994), where the expected response is simply proportional to
the latent state intensity:
$$E(X)=\alpha(\theta-\delta)$$
where $\theta$ and $\delta$ are unknown person (state or attitude) and item (threshold or mean) parameters, and $\alpha$ a scale (or loading) parameter.
A boundary effect
Practical consequences
- Factors are not dimensions: We may well have one dimension and several factors. This is the extra-factor phenomenon (Davison, 1977; Van Schuur & Kiers, 1996).
- Factors and dimensions are the same only in the (unrealistic) linear case.
- In the nonlinear case, factor techniques will likely extract too many factors.
- In this situation, we look for principal curves, not components (Hastie & Stuetzle, 1989; Tibshirani, 1992).
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
The meaning of components: Simulated data
The meaning of components: PCA solutions
The meaning of components: Eigenvectors shapes
The meaning of components: Simulated data
First conclusions
- PCA, as a particular case of a Karhunen–Loève transform automatically finds the best orthogonal basis that minimizes square reconstruction error on finite one-dimensional signals.
- Finding common components by minimizing error variance tend to recover smooth components.
- While signal theory looks for eigenfunctions of time, psychometrics/sensometrics looks for eigenfunctions of some unknown latent attitude or preference.
- An analytic form for these eigenfunctions may sometimes be derived for some a priori known generative processes, such as 1D Markov or Wiener processes (Dony, 2000, p. 10), in which cases sine bases emerge.
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
A dynamical perspective
Theoretical background
- The Transactional Model of Stress and Coping (Lazarus & Folkman, 1984) states that emotional reaction to a stressful event is determined by the appraisal of available coping ressources.
- The theory of Learned Helplessness (Maier & Seligman, 1976) describes how repeated failure to cope with stressors, with no feeling of control or understanding, can lead to a depressive state.
- The General Adaptation Syndrom proposed by Selye (1956) also describes the stages of reaction to stress as a sequence from an alarm state, through resistance, to potentially exhaustion and depression.
Expected response functions
Expected PCA solution
Principal curves
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
A folding artefact
The International Affective Picture System
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
A dynamical multi-process model
- In the line of Item Response Theory, responses are considered determined by a single latent dimension, summarized as an attitude or state parameter ($\theta$).
- We assume that response to a emotion items are determined by two latent
response processes $x$ (activation) and $y$ (inhibition or exhaustion), which are dynamically related, in the following way:
\[\begin{cases} \frac{dx}{d\theta}=\alpha x(\theta)\color{#0587c4}{-\gamma y(\theta-\delta)}\\ \frac{dy}{d\theta}=\beta y(\theta) \end{cases}\] with $\alpha$, $\beta$ et $\gamma$ positive factors, and $\delta$ a shifting parameter.
- Interpretation : With positive change rates $\alpha$ and $\beta$, $x$ and $y$ are increasing with $\theta$, $y$ exerting an inhibitory action over $x$, possibly with some delay/shifting $\delta$, along a common dimension $\theta$.
Boundary constraints
- Solution functions for this type of differential equations are well-known to be linear combinations of exponentials (e.g. compartment models).
- This is not suited to the modeling of bounded data (i.e. binary data or continuous bounded scales).
- Boundary constraints are imposed to ensure that the result remains in the $[0;1]$ range: \[\begin{cases} \frac{dx}{d\theta}=\left[\alpha x(\theta)-\gamma y(\theta-\delta) \color{#0587c4}{x(\theta)}\right]\color{#0587c4}{[1-x(\theta)]}\\ \frac{dy}{d\theta}=\beta y(\theta)\color{#0587c4}{[1-y(\theta)]} \end{cases}\]
Solution functions
- Upon integrating this system, we get for
$x(\theta)$ the generic expression
(Noel, 2017):
$$ x(\theta)=\frac{\exp\left[\alpha(\theta-\delta)+\lambda\right]}{\color{#0587c4}{\left\{ \exp[\beta(\theta-\delta)]+1\right\} ^{\frac{\gamma}{\beta}}}+\exp\left[\alpha(\theta-\delta)+\lambda\right]} $$
Parameter interpretation
\[
\tiny x(\theta)=\frac{\exp\left[\alpha(\theta-\delta)+\lambda\right]}{\left\{
\exp\left[\beta(\theta-\delta)\right]+1\right\}
^{\frac{\gamma}{\beta}}+\exp\left[\alpha(\theta-\delta)+\lambda\right]}
\]
The Beta Asymmetric Unfolding Model (BAUM)
- A Beta response model may be defined as
$X_{ij}\sim Beta(m_{ij},n_{ij})$, for subject $i$ and item $j$, with:
$$\begin{cases} m_{ij}&=\exp\left[\alpha_j(\theta_i-\delta_j)+\lambda_j\right] \\ n_{ij}&=\left\{ \exp\left[\beta_j(\theta_i-\delta_j)\right]+1\right\}^{\frac{\gamma_j}{\beta_j}} \end{cases} $$
- The expected response function (ICC) is
then given by:
$$ E(X_{ij}|\theta_{i})=\frac{m_{ij}}{m_{ij}+n_{ij}}=\frac{\exp\left[\alpha_{j}(\theta_{i}-\delta_{j})+\lambda_{j}\right]}{\left\{ \exp\left[\beta_{j}(\theta_{i}-\delta_{j})\right]+1\right\}^{\frac{\gamma_{j}}{\beta_{j}}}+\exp\left[\alpha_{j}(\theta_{i}-\delta_{j})+\lambda\right]} $$
A generic model
- Within the generic model: \[ {\tiny E(X_{ij}|\theta_{i})=\frac{\exp\left[\alpha_{j}(\theta_{i}-\delta_{j})+\lambda_{j}\right]}{\left\{ \exp\left[\beta_{j}(\theta_{i}-\delta_{j})\right]+1\right\} ^{\frac{\gamma_{j}}{\beta_{j}}}+\exp\left[\alpha_{j}(\theta_{i}-\delta_{j})+\lambda_{j}\right]}} \]
- ... fixing $\alpha=\beta=1$ and $\gamma=0$ brings us back
to the Beta Response Model1:
\[ E(X_{ij}|\theta_{i})=\frac{\exp\left(\theta_{i}-\delta_{j}+\lambda_{j}\right)}{1+\exp\left(\theta_{i}-\delta_{j}+\lambda_{j}\right)} \]
- ... fixing $\alpha=\beta=1$ and $\gamma=2$ brings us back (almost) to the Beta Unfolding Model2 : \[ E(X_{ij}|\theta_{i})=\frac{\exp\lambda_{j}}{\exp\lambda_{j}+\exp\left[\theta_{i}-\delta_{j}\right]+\exp\left[-\left(\theta_{i}-\delta_{j}\right)\right]\color{#0587c4}{+2}} \]
Modeling the variance
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
A suspicion of a nonlinear relationship
A Beta Unfolding Model
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
Processes and stages of behavioral change
| I. Precontemplation (non motivation) |
II. Contemplation (expect change within 6mo) |
III. Preparation (expect change within 30d) |
IV. Action (quit, last 6mo) |
V. Maintenance (quit, more than 6mo ago) |
|---|---|---|---|---|
| 01 - Social liberation (Perception of non-smokers' behavior) |
||||
| 02 - Environmental reevaluation (reassess impact on environment) |
||||
| 03 - Emotional relief (express negative feelings) |
||||
| 04 - Consciousness raising (taking information on quitting smoking) |
||||
| 05 - Sef-reevaluation (reassess one's behavior and values) |
||||
| 06 - Self-liberation (Decision, will power) |
||||
| 07 - Stimulus control (Remove any cue or incentive) |
||||
| 08 - Helping relationships (Rely on significant others) |
||||
| 09 - Reinforcement management (Find alternative sources of satisfaction) |
||||
| 10 - Counter-conditioning (Find replacements and substitutes) |
||||
Cumulative vs. unfolding models of change
An empirical study
- $N=614$ students from Schools of Nursing in France responded to the Self-Change Strategies questionnaire (Etter & al., 2000) at the beginning of their first year.
- The questionnaire includes 8 cognitive items et 12 behavioral items, rated on a 0-100% agreement visual analogue scale.
- Three models have been tested : The cumulative BRM (AIC=-8478.144), the symmetric BUM (AIC=-10401.1) and the asymmetric BAUM (AIC=-10754.2).
Discrete vs. continuous models of change
Measuring change readiness
Note: Figures are median locations by stage.
End
Thank you for your attention.
yvonnick.noel@univ-rennes2.fr
Contents
- An example: The analysis of mood states and emotions
- Dynamical psychometrics
- Modeling behavior change dynamics
• • • •
• • •
•
The Beta distribution
Moments
- The expected response in the Beta is: \[E(X;m,n)=\mu=\frac{m}{m+n} \]
- The modal response is: \[Mo(X;m,n)=\frac{m-1}{m+n-2} \]
- Variance is given by: \[ V(X;m,n)=\frac{mn}{(m+n)^{2}(m+n+1)}=\mu(1-\mu)\left[\frac{1}{\color{#0587c4}{m+n}+1}\right] \]