Writing Increases Precision-Weighted Inference of Conceptual Organization: A Bayesian-Brain Active-inference Model of the Writing-over-Speaking Advantage in Analytic Thinking

1. Introduction

Language serves as a fundamental tool for organizing and expressing thoughts. It not only enables communication but also reflects underlying cognitive processes that guide how individuals interpret, organize, and interact with the world [1]. Consider, for example, a picture-description task, such as the thematic apperception test [2]. In general, in this task participants produce short narratives about a visual depiction (e.g., pictures or drawings). The basic trial consists of two stages. The participant expects the presentation of the visual depiction, and once the visual depiction is shown the participant produces a short narrative about its content.

The narrative’s production entails at least two stages: prelinguistic and linguistic stages. In the prelinguistic stage, the speaker constructs an internal representation of the picture content whereas in the linguistic stage the speaker translates or encodes that representation into words [3,4,5,6,7]. These stages are not unique to speaking. The analogue in writing-production models is the planning, idea-generation, or content-generation stage, in which writers generate, select, and organize ideas before translating them into written language [8,9,10,11,12,13,14,15,16,17].

Regardless of the language-production modality, the prelinguistic stage refers to the unobservable conceptual apprehension [18,19], conceptual or event representation [19,20], or conceptual organization (CO) [21] in the mind of the speaker or writer, which is subsequently grammatically encoded [4]. Although these terms originate in different theoretical traditions, they all refer to an internal semantic representation of external or internal stimuli. In this manuscript, the term CO is used as an encompassing construct for this prelinguistic semantic organization.

Despite the distinction between prelinguistic and linguistic stages, the structure of the language produced during the linguistic stage can reveal prelinguistic patterns of CO and broader cognitive traits, including abstract reasoning ability [22], working-memory load [23], and individual differences in personality, emotional expression, and mental health [24,25,26]. Advances in computational linguistics and natural-language processing have made it possible to quantify these patterns objectively [27]. One such measure is the analytic thinking score (ATS), developed within the Linguistic Inquiry and Word Count framework, LIWC, [28,29].

The ATS is a continuous variable ranging from 0 to 100 that indexes the relative degree of categorical versus narrative thinking expressed in language. High ATS values are associated with categorical function words, especially articles and prepositions, whereas lower values are associated with more narrative or context-dependent function words, including adverbs, pronouns, negations, auxiliary verbs, and conjunctions. For example, consider the text “The car by the house near the building was in the garage. He drove it there because they felt really scared and could not stay inside anymore”. The first sentence is article- and preposition-dense and therefore receives a high ATS (100), whereas the second sentence contains more narrative/context-dependent function words and therefore receives a low ATS (0.05). The overall ATS (66.02) reflects the relative balance of these linguistic markers.

ATS has been assigned psychometric [25,27]and clinical significance [21,30]. For example, Silva, et al. [30] and Limongi, et al. [21] showed that individuals with first-episode schizophrenia produced spoken responses with significantly lower ATS than healthy controls, suggesting that reduced linguistic structure may reflect conceptual disorganization, or lower CO. Notably, this effect emerged despite no group differences in the overall proportion of function and content words, emphasizing ATS as a stylistic marker of thought organization rather than merely a marker of lexical quantity.

Observational studies indicate that ATS differs across spoken and written registers, with higher scores typically observed in written language [31,32]. Moreover, university students whose essays contain a greater proportion of categorical function words relative to narrative function words, that is, higher ATS, tend to achieve higher academic grades [22]. More recent work also links ATS in written registers to cognitive variables [33]. These findings suggest that writing may provide especially favorable conditions, for example increased attentional focus for the generation of organized CO. However, the psychological status of ATS has been established primarily through correlational analyses between function-word use and presumed cognitive variables [22,33]. Furthermore, no study has directly compared ATS across spoken and written language modalities under controlled laboratory conditions while also formalizing the underlying neurocognitive mechanism.

The present manuscript addresses this gap by developing a Bayesian-brain, active-inference model of the ATS as a linguistic index of the prelinguistic CO. The paper proceeds in four steps. First, it establishes the idea of precision-weighted inference over CO through a succinct high conceptual link between the words-as-attention assumption in natural language processing, CO, and attention as a synaptic gain mechanism. Second, it formalizes this link at Marr’s [34] three levels of analysis within an active-inference (Markov decision process, MDP) model. Third, it instantiates the model through a laboratory-controlled experiment. Finally, it assesses the construct validation of the MDP model within the framework of Variational Laplace, free energy, and Bayesian model selection.

From Words-as-Attention to Attention as Synaptic Gain During Precise Inference of CO

Traditionally, natural-language processing approaches for inferring unobserved cognitive processes from observed fine-grained linguistic features, such as word counts, have assumed that words provide observable evidence of attention. This idea is often described as the words-as-attention assumption [35]. Eye-movement research [18,36] has also provided evidence for the fundamental role of attention during the unobserved prelinguistic stage of language production, when speakers and writers selectively sample and organize information before encoding it into language. Together, these lines of research suggest that ATS derived from computational analyses of linguistic registers may reflect attentional foci that emerged during the unobservable or hidden prelinguistic CO and were later encoded into observable language.

From a neurobiological perspective, attention can be understood as synaptic gain control. Synaptic gain refers to the responsiveness of neuronal populations to incoming input: when gain is increased, the same sensory input produces a stronger postsynaptic response and has greater influence on downstream processing. In predictive-processing and active-inference accounts, attention is often interpreted as increasing the gain of neuronal populations encoding prediction errors, thereby making selected sensory signals more precise, or more influential, during perceptual inference [4,5,6]. Heuristically, focusing attention on a stimulus means giving that stimulus more weight when the brain updates its interpretation about the stimulus content.

The picture-description task provides a suitable experimental design for assessing whether ATS reflects attention during prelinguistic CO. In this task, participants are cued to either speak or write a narrative about the content of a picture. The central claim is not that writing directly produces higher ATS. Rather, the speaking or writing cue helps the participant interpret what kind of CO is required for the task. In the formal model introduced below, this cue-guided interpretation is represented as the precision with which speaking or writing cues guide inference over CO. When the cue is treated as clear and reliable (i.e., precise), it produces stronger confidence in the corresponding form of CO.

Under this formulation, high ATS is expected when the participant becomes highly confident in a writing-associated form of CO: that is, a more stable, categorical, and analytically organized way of preparing the picture content for language. Conversely, low ATS is expected when the participant becomes highly confident in a speaking-associated form of CO, which is assumed to be more narrative and context-dependent. Therefore, the writing-over-speaking advantage in analytic thinking could be interpreted as the behavioral expression of more precise cue-guided inference over CO, rather than as a direct consequence of writing per se.

The process described above imposes a computational problem for the participant. During picture description, the participant must determine what kind of conceptual organization the task requires: a more categorical, writing-associated form of CO or a more narrative, speaking-associated form of CO. This determination cannot be read directly from the picture itself. Rather, it must be inferred by combining the speaking or writing cue, prior expectations about the picture, and incoming sensory information from the picture. The participant must also determine how much weight, or confidence, to assign to the speaking or writing cue when using it to guide CO. In other words, the task requires not only inference over what form of CO is currently relevant, but also inference over the precision with which the cue should guide that CO. In the following section, we formalize the solution of these problems in terms of Marr’s levels of analysis [34] applied to active inference and the Bayesian brain.

The Bayesian Brain and the ATS Through Marr’s Levels of Analysis

Marr’s computational, algorithmic, and implementational levels of analysis provide a useful framework for linking cognitive theories, computational models, and neural mechanisms [37,38]. The computational level specifies the problem an agent must solve and why that problem matters. In the present case, the problem is to infer the CO state under which a picture-description response is generated. The algorithmic level specifies the procedures by which this inference is performed. The implementational level specifies how the algorithm could be realized neurally.

In the present formulation, the computational level is expressed as Bayesian inference framed within a two-timestep Markov decision process (MDP). Here, the participant is modeled as an active-inference agent that infers a hidden CO state from observed speaking and writing cues. Attention enters the model as the precision with which observed cues are mapped onto hidden CO states. The algorithmic level corresponds to marginal message passing; whereby posterior beliefs are iteratively updated to minimize variational free energy. The implementational level corresponds to a neural-process interpretation of the same updates, in which prediction-error signals and precision-weighted synaptic gain provide a plausible cortical implementation. Prediction error therefore bridges levels: it is the formal quantity that drives belief updating and the signal proposed to be encoded by neuronal populations in the neural implementation. Below, we detail all three levels of analysis.

Computational Level of Analysis: Inferring Latent CO States Through Bayes Theorem

Bayesian approaches to brain function, commonly referred to as the Bayesian-brain hypothesis [39,40,41,42,43,44,45,46] propose that the brain does not passively register the world but infers the hidden causes of sensory input. Because sensory evidence is often ambiguous, incomplete, or noisy, perception requires the integration of prior expectations with current evidence. A prior belief refers to what the system expects before new evidence is considered. Sensory evidence refers to the information currently available to the organism. A posterior belief is the updated belief that results from combining prior expectations with sensory evidence. Formally, this updating process can be described as the inversion of a generative model using Bayes theorem:

$$P\left(CO\mid o\right)={\displaystyle \frac{P\left(o\mid CO\right)P\left(CO\right)}{P\left(o\right)}}$$

Here, CO denotes a hidden state, o denotes an observation (i.e., speaking or writing cue), P(CO) is the prior belief over hidden CO states, P(o | CO) is the likelihood: the probability of observing a particular speaking or writing cue if a given CO state were present. P(o) is the model evidence, and P(CO | o) is the posterior belief over hidden states after observing the speaking or writing cue. In words, the active-inference agent infers the most likely hidden CO state by combining what it expected before the observation of the speaking or writing cue with how strongly the observation supports each candidate CO state.

Active inference extends this Bayesian account by specifying how organisms use generative models to perceive and act. In active inference, there are four main families of models: static perception, dynamic perception, dynamic perception with policy selection, and dynamic perception with flexible policy selection [47]. In all four model families, perception corresponds to updating beliefs so that they better explain sensory observations, whereas action corresponds to changing sensory input so that it becomes consistent with expected or preferred states. In this implementation, the model falls within the family of dynamic perception and is specified as a two-timestep MDP. It therefore formalizes how active-inference agents infer CO states from sensory speaking and writing cues, not how they select among alternative actions.

The two-timestep MDP shown in Figure 1 realizes dynamic perception as inference over latent CO states. The hidden-state factor represents the level of CO under which the active-inference agent is preparing to describe the picture. Each trial begins in a start state, after which the agent uses the observed speaking or writing cue to infer whether the current picture-description context is more likely to support low or high CO. The hidden-state space is therefore start, low CO, and high CO.

The observation modality contains three possible outcomes: a start cue, a speaking cue, and a writing cue. The likelihood matrix (A) specifies the probability of each observed cue conditional on each hidden CO state. The (D) vector fixes prior beliefs over the initial state, whereas the (B) matrix allows transitions from the start state to either a low-CO or high-CO state.

The likelihood matrix illustrates how the present model adopts the active-inference account of attention as the precision-weighting of sensory evidence. In active inference, attention is treated as the inferred precision, or expected fidelity, of the mapping between hidden states and observations [48,49,50,51,52,53]. In the present model, this principle is applied to CO: the attention-related parameter AP controls the precision and directionality with which latent CO states are mapped onto observed speaking or writing cues.

Formally, the likelihood matrix specifies the probability of observing a start, speaking, or writing cue conditional on the current hidden CO state. The agent inverts this mapping to infer the most probable CO state from the observed speaking or writing cue. When AP = 0.50, speaking and writing cues are equally likely under either CO state, making the mapping maximally ambiguous. Thus, the observed cue provides no differential evidence for whether the agent is in a low-CO or high-CO state. As AP increases above 0.50, the mapping becomes increasingly diagnostic in the hypothesized direction: the speaking cue provides stronger evidence for a low-CO state, whereas the writing cue provides stronger evidence for a high-CO state. Conversely, as AP decreases below 0.50, the mapping becomes increasingly diagnostic in the opposite direction: the speaking cue provides stronger evidence for a high-CO state, whereas the writing cue provides stronger evidence for a low-CO state. In this sense, AP does not represent ATS itself, but the diagnostic precision with which speaking or writing cues disclose the latent CO state that is later expressed linguistically in ATS.

This formulation clarifies how AP relates to ATS. AP does not directly increase ATS. Rather, AP controls the precision and directionality of the mapping between latent CO states and observed speaking or writing cues, thereby determining how strongly an observed cue updates posterior beliefs about the latent CO state. The posterior belief over CO is the immediate computational bridge to ATS. In the present interpretation, high and low ATS are treated as stochastic behavioral readouts of posterior beliefs over latent CO states: a stronger posterior belief in the high-CO state increases the probability of producing a high-ATS text, whereas a stronger posterior belief in the low-CO state increases the probability of producing a low-ATS text. This can be expressed heuristically as:

$$P\left(y=HighATS\right)\approx q\left(s=HighCO∣o\right)$$

where (y) denotes the observed linguistic outcome, (s) denotes the latent CO state, and (o) denotes the observed speaking or writing cue.

As posterior confidence in a high-CO state approaches 1, the active-inference agent is assumed to enter an attentional set that supports more stable, categorical, and analytically organized prelinguistic CO, which is expressed downstream as higher ATS. Conversely, as posterior confidence in a low-CO state approaches 1, the agent is assumed to enter an attentional set that supports less stable or less analytically organized CO, which is expected to yield lower ATS. The behavioral writing-over-speaking advantage therefore arises when the mapping is precise in the hypothesized direction, such that writing cues provide stronger evidence for high-CO states than speaking cues.

Algorithmic level of analysis: updating beliefs about CO states through marginal message passing

At the algorithmic level, belief updating over CO states is computed through marginal message-passing [54]. The two relevant updating equations can be written as follows:

$${\mathbf{s}}_{\tau =1}=\sigma \left({\displaystyle \frac{1}{2}}\left(\mathrm{l}\mathrm{n}\mathbf{D}+\mathrm{l}\mathrm{n}{\mathbf{B}}_{\tau }^{†}{\mathbf{s}}_{\tau +1}\right)+\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau }\right)$$

$${\mathbf{s}}_{\tau =T}=\sigma \left({\displaystyle \frac{1}{2}}\left(\mathrm{l}\mathrm{n}{\mathbf{B}}_{\tau -1}{\mathbf{s}}_{\tau -1}\right)+\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau }\right)$$

At the first timestep, posterior beliefs over CO states are updated by combining the prior message from (D), the backward temporal message from the second time point, and the likelihood message supplied by the observed speaking or writing cue. At the second timestep, beliefs are updated by combining the forward message from the first time point with the likelihood message. In both equations, $\sigma$ denotes the softmax normalization that converts log-probability messages into posterior beliefs over hidden CO states.

The likelihood message ($\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau }$) is the component of the update through which the observed speaking or writing cue supplies evidence for the latent CO state. The strength and directionality of this evidence are controlled by AP, which determines how precisely latent CO states are mapped onto observed speaking or writing cues in the likelihood matrix. Thus, AP specifically modulates the sensory-evidence term in the message-passing update, while the (D) and (B) terms encode prior and temporal constraints on state inference.

This algorithmic formulation is important because the model contains two distinct time scales. The task itself has two time points, but the inference performed within each time point can involve multiple internal message-passing iterations. Thus, as explained below, a two-timestep MDP can implement an iterative neural updating process while processing a single speaking or writing cue.

Neural (implementational) Level of Analysis

In the neural process theory of active inference [49], the brain implements belief updating through a prediction-error formulation of message passing [48,50]. In predictive-processing formulations, neuronal populations encoding expectations about hidden states generate predictions, whereas prediction-error populations encode the mismatch between incoming evidence and current beliefs. These prediction errors update neuronal activity until posterior beliefs best explain the sensory evidence. Canonical-microcircuit accounts further motivate the interpretation of belief updating in terms of layered cortical message passing and precision-weighted synaptic gain [51,52].

Figure 2 depicts the simplified neural implementation used in the present model. The computer screen presents a clear picture-description stimulus together with a speaking or writing cue. However, the sensorium registers this input as a noisy sensory observation. Within the present formulation, lower diagnostic precision in the cue–CO mapping corresponds to less informative sensory evidence about the latent CO state, whereas higher diagnostic precision corresponds to a less ambiguous sensory message. For example, in the hypothesized direction of the present model, AP = 0.8 provides stronger evidence for the corresponding latent CO state than AP = 0.6. Feedforward sensory evidence projects toward the granular layer, where precision-weighted prediction-error messages are computed. These messages update state representations associated with the inferred CO state in supragranular layers.

In the picture-description task, prediction-error signals carry evidence about latent CO. A writing cue or speaking cue is compared against predictions generated from current beliefs about the latent CO state. The resulting prediction error updates neuronal activity encoding posterior beliefs about whether the agent is in a low-CO or high-CO state. AP can therefore be interpreted as a gain parameter on CO-relevant prediction errors. It is important to note that the figure is schematic: it is intended to show how active-inference message passing can be related to cortical layers, not to assign the entire model to a literal one-to-one anatomical circuit.

For the first and second timesteps respectively, the prediction-error formulation can be expressed as the difference between incoming model-based evidence and the current belief state:

$${\mathbf{P}\mathbf{E}}_{\tau =1}\leftarrow {\displaystyle \frac{1}{2}}\left(\mathrm{l}\mathrm{n}\mathbf{D}+\mathrm{l}\mathrm{n}{\mathbf{B}}_{\tau }^{†}{\mathbf{s}}_{\tau =2}\right)+\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau =1}-{\mathbf{s}}_{\tau =1}$$

$${\mathrm{P}\mathrm{E}}_{\tau =2}\leftarrow {\displaystyle \frac{1}{2}}\left(\mathrm{l}\mathrm{n}{\mathbf{B}}_{\tau =1}{\mathbf{s}}_{\tau =1}\right)+\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau =2}-{\mathbf{s}}_{\tau =2}$$

For brevity, we explain the neuronal process at the second timestep (Figure 2). The prediction error (PE) signal results from the algebraic sum of the agent’s belief about the CO state transition before observing the speaking or writing cue, ${\displaystyle \frac{1}{2}}\left(\mathrm{l}\mathrm{n}{\mathbf{B}}_{\tau =1}{\mathbf{s}}_{\tau =1}\right),$the likelihood message after observing either the writing or speaking cue, $\mathrm{l}\mathrm{n}{\mathbf{A}}^T{\mathbf{o}}_{\tau =2},$ and the current posterior CO state belief, ${\mathbf{s}}_{\tau =2}$. The first two messages are excitatory, and the third message is inhibitory. Prediction error therefore expresses the mismatch between model-based evidence and the agent’s current posterior belief over the CO state.

Prediction error then updates the neuronal activity, or membrane voltage, underlying posterior belief. In continuous form, this can be written as:

$${\mathbf{v}}_{\tau =2}^{\left(k+1\right)}\leftarrow {\mathbf{v}}_{\tau =2}^{\left(k\right)}{+\mathbf{P}\mathbf{E}}_{\tau =2}^{\left(k+1\right)}$$

$${\mathbf{s}}_{\tau =2}^{\left(k+1\right)}=\sigma \left({\mathbf{v}}_{\tau =2}^{\left(k+1\right)}\right)$$

Here, (v) denotes neuronal activity or membrane voltage, and (k) indexes belief-updating iterations. Importantly, (k) does not denote task time. Even in a two-timestep MDP, the system can perform multiple internal neural updates while processing a single observation. After each update, posterior beliefs over CO states are obtained by applying a softmax function to the updated voltage. The iterative process continues until prediction error is minimized and posterior beliefs settle. At convergence, the posterior belief over CO reflects the hidden organization state that best explains the speaking or writing cue. This posterior belief over CO is then interpreted as the latent inferential state expressed downstream in ATS.

Summary of the Model

The central thesis is that speaking and writing are not merely external conditions that directly alter analytic thinking. Rather, they are observed speaking or writing cues that provide sensory evidence about latent states of CO. The attention-related likelihood precision parameter, AP, modulates the precision and directionality of the likelihood mapping between latent CO states and observed speaking or writing cues, thereby shaping posterior beliefs about whether the current picture-description context is more consistent with a low-CO or high-CO state. These posterior beliefs constitute the immediate computational bridge to ATS: the MDP does not model ATS directly, it models the latent prelinguistic CO stage that is expressed downstream in in the linguistic stage.

Once the agent infers a low-CO or high-CO state, this posterior belief constrains the attentional and CO under which picture-derived evidence is sampled, organized, and prepared for linguistic encoding. ATS is therefore interpreted as the downstream linguistic expression of CO inferred through precision-weighted processing of speaking or writing cues. The causal chain can be summarized as follows:

Production cue→A(AP)→q(CO state)→attentional set→linguistic encoding→ATS

In this chain, (A(AP)) is the likelihood mapping controlled by the attention-related precision parameter. Formally, this likelihood specifies the probability of observing a speaking or writing cue conditional on the latent CO state. During inference, the agent inverts this mapping to infer the posterior probability of low versus high CO from the observed cue. The term q(CO state) denotes this posterior belief over latent CO states. The attentional set is the cognitive-neurobiological state associated with this posterior belief. Finally, ATS is the observable linguistic marker produced after the inferred CO state has been translated into language. In the following section, we report a laboratory-controlled experiment that instantiates the current formulation.

2. Materials and Methods

Participants

A sample of N = 17 (13 female) with a mean age of 20 (SD= 2.08) healthy subjects from Brandon University participated in the study. Fourteen participants (82%) identified English as their first language. Participants were recruited using posters, online advertising and through in-person outreach and received compensation of fifty dollars (gift card) at the end of the experimental session. Participants were required to be registered as an undergraduate or graduate student in any department or program at Brandon University, be at least 18 years of age and considered a ‘healthy subject’ – being they had no history of any neurological or mental health disorders. There were no other inclusion criteria. Participants provided written informed consent adhering to the regulations of Brandon University Research Ethics Committee. Sample size estimation was based on sequential analysis and optional stopping [55,56].

Optional Stopping for Sample Size Definition

After collecting data from 10 participants, we fit Bayesian ANCOVA models to the ATS, including condition as a fixed effect, participant as a random effect, and number of words as a covariate. All ANCOVA models were implemented in JASP [57]. We defined a stopping criterion based on BF₁₀ > 10, indicating strong evidence [58] in support of higher ATS in the writing condition compared to the speaking condition Data collection proceeded one participant at a time, with BF₁₀ recomputed after each addition, until the threshold was reached.

Procedure

Participants were seated at a computer desk and provided verbal instructions of the experimental procedure. All participants received the same instructions and were informed the purpose of the study was to collect discourse samples while viewing pictures. Written instructions were provided on the computer screen before beginning two familiarization trials. Specifically, participants were instructed: “In this task, you will be shown a series of images. For each image, we ask that you carefully observe it while at the same time describing what you see. Describe the picture with as much detail as you can. Tell us what you see in the image, describe any elements you wish, and what you think might be happening. At times, you may be prompted to describe the image out loud. At other times, you may be asked to type your response on the computer keyboard. Please provide as much detail as possible in either format. There is no right or wrong answer; we are simply interested in your observations and thoughts. You will have a 2-minute window to respond to each image. You may stop early if you have no further comments. After the 2-minutes is up there will be an opportunity to rest before the next image is presented.”. The researcher remained in the room for the entire experiment.

Stimuli

Experimental stimuli consisted of ten images taken from the thematic apperception test bank [2] and were presented on a Dell Pro 24 Plus (P2425H) computer monitor positioned approximately 30 inches away from the participant. All pictures were presented at a consistent size (portrait, 5x7 inches) and displayed on a neutral grey background. Directly below the image, the language condition cue was indicated using a single capitalized letter (S for speak, W for write) in black type font. The image and language condition cue were presented simultaneously to the participant. Prior to being exposed to the experimental block, participants completed a familiarization trial using two black and white images that did not belong to the TAT test bank and had the opportunity to ask any questions regarding the task before moving onto the experimental stimuli.

Experimental Task

Participants completed an experimental block viewing 10 images, responding to 5 in written modality and 5 in spoken modality, with the opportunity to rest after images. Image order and response modality was randomized and counterbalanced across participants. Participants were simultaneously presented with an image and response modality cue and had 120 seconds to respond to each image. As specified in the task instructions, participants were requested to describe the image in as much detail as possible and that they could create a narrative or story about what they saw. Spoken responses were audio recorded using a headset-mounted microphone and were later transcribed by the researcher. Written responses were typed using the keyboard and automatically logged into an excel file on the computer system. The task was built using PsychoPy [59],

Data Processing and Analysis

Speech samples were transcribed and preprocessed to remove fillers and stutters. Written samples were corrected for typos and abbreviations. All 170 discourse samples were formatted as individual plain text files. Using LIWC-22 [28], we obtained trial-wise ATS. At the subject level and collapsed across conditions, ATS values were discretized based on each participant’s median distribution; scores equal to or below the median were categorized as low ATS, whereas scores above the median were categorized as high ATS. We used SPM12 (http://www.fil.ion.ucl.ac.uk/spm/) and modified scripts available in [47,60] to specify and estimate the parameters of the two-timestep MDP model described and explained in the previous section.

3. Results

Behavioral Results

Table 1 summarizes the behavioral results. Mean ATS was higher in the writing condition than in the speaking condition. A Bayesian ANCOVA model comprising fixed effect of condition, random effect of subject and trial, and numbers of words as covariate of no interest confirmed this difference and ruled out an effect of number of words (i.e., the model including the covariate received less support, BF₁₀ = 8.80 × 10⁸, than the model without the covariate, BF₁₀ = 2.04 × 10⁹ 10. Table 2 shows the estimates of the winning model. We further fit a Bayesian generalized linear mixed effects model (binomial family) to confirm that the ATS difference between conditions remained after discretization (Table 3 shows the estimates in logit units, and Figure 3 shows the transformed estimates to probabilities).

Computational Model Results

Model Parameter Estimates and Parametric Empirical Bayes (PEB)

Table 4 shows the subject-level parameter estimates of the MDP model. The subject-level posterior estimates of the attention-related parameter AP, transformed from logit space to probability space, ranged from 0.50 to 0.72. Descriptively, the mean transformed estimate was (M = 0.59), (SD = 0.07), indicating that the estimated likelihood mapping was above the non-diagnostic value of 0.50.

To formally assess whether AP exceeded its non-diagnostic value at the group level, we submitted the first-level posterior estimates to a second-level Parametric Empirical Bayes model [61,62]. Importantly, AP was estimated in logit space at the first level and was transformed into probability space only for interpretation. Therefore, in the PEB model and associated SPM output, the relevant null value is 0, not 0.50. This is because a logit-scale value of 0 corresponds exactly to (AP = 0.50) on the probability scale. Thus, testing whether the group-level PEB estimate is greater than 0 in logit space is equivalent to testing whether the transformed AP parameter is greater than 0.50 in probability space.

The PEB model yielded a positive group-level posterior estimate (AP = 0.657), after applying the transformation to a probability scale. The posterior probability that the group-level logit parameter was greater than 0 was approximately 1.00, providing strong evidence that the estimated attention-related likelihood precision parameter exceeded its non-diagnostic value of 0.50 on the probability scale (Figure 4). In the present model, this indicates that, at the group level, the likelihood mapping was diagnostic in the hypothesized direction, with writing cues providing stronger evidence for high-CO states and speaking cues providing stronger evidence for low-CO states.

Construct validity: Bayesian Model Selection

Because the present MDP embodies the theoretical construct of latent conceptual organization, operationalized as precision-weighted inference from speaking or writing cues to CO states, we assessed its construct validity by comparing it against a simpler descriptive model of ATS estimated under Variational Laplace. This comparison was motivated by the distinction between describing a condition effect and explaining the latent process that could have generated it. A linear model can test whether ATS differs between speaking and writing, but it treats production condition as an observed predictor acting directly on ATS. It therefore quantifies the writing-over-speaking effect without formalizing the hidden inferential mechanism through which participants use speaking or writing cues to infer latent CO states, establish an attentional set, and generate linguistic output.

By contrast, the active-inference MDP formalizes the hypothesis that speaking and writing are not merely external response formats but observed cues that provide evidence about latent states of CO.

Variational Laplace [63] provides a common Bayesian estimation framework for this comparison because it returns an approximation to the log model evidence, or variational free energy, for each fitted model. This is important because model evidence evaluates accuracy and complexity jointly. A model is favored only when its gain in explanatory accuracy justifies its additional complexity. Therefore, comparing the variational free energies of the linear model and the MDP provides a principled test of whether the mechanistic active-inference model explains the ATS data better than a simpler descriptive account.

At the group level, we used random-effects Bayesian model selection following Rigoux, et al. [64]. This framework is appropriate because it does not assume that the same model generated every participant’s data. Instead, it treats model identity as a random effect and estimates the expected frequency with which each model occurs in the population. This is especially suitable for behavioral and cognitive data, where participants may differ in the extent to which their responses are governed by the hypothesized latent mechanism. The protected exceedance probability was used as the main index of model superiority because it estimates the probability that one model is more frequent than the competing model while correcting for the possibility that apparent differences in model frequencies arise by chance. The Bayesian omnibus risk was also reported because it estimates the probability that the apparent model-frequency differences are not meaningful.

Random-effects Bayesian model selection favored the active-inference MDP over the Variational Laplace linear model. The MDP showed a protected exceedance probability of 0.95, indicating a high probability that it was the more frequent model in the population after correcting for chance differences in model frequency. The Bayesian omnibus risk was low, (BOR = 0.08), indicating a relatively small probability that the observed differences in model frequency reflected random variation. Together, these results indicate that the MDP provided a better account of the ATS data than the Variational Laplace linear model after accounting for model complexity.