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ISSN 0439-755X
CN 11-1911/B
主办:中国心理学会
   中国科学院心理研究所
出版:科学出版社

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    Theory and History of Psychology
    The essence of bounded rationality and debate over its value
    LIU Yongfang
    2022, 54 (11):  1293-1309.  doi: 10.3724/SP.J.1041.2022.01293
    Abstract ( 4675 )   HTML ( 126 )  
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    Bounded rationality theory derives from contemporary cognitive psychology, manifests itself in economics, and radiates to many disciplines. However, different opinions exist on what bounded rationality is and what it means to people, not only causing confusion in theory but also bringing confusion in practice.

    The purpose of this study is to: (1) clarify the essential meaning of bounded rationality from the philosophical and historical backgrounds of human rational evolution; (2) put forward different views on the value of bounded rationality; (3) summarize the far-reaching historical significance and theoretical value of existing achievements.

    The author points out that bounded rationality is not the optimization under constraint, not to mention the irrationality. In essence, it is an objective description of the level of human rational evolution and development so far, that is, human beings are rational either in the attitude to reality or in the ability to recognize and transform reality. However, limits to human rationality are observed. Bounded rationalists question popular rationalism in contemporary social science and the reliability of the methodology and knowledge system derived from it, but they do not question rationality itself. They eliminate the dualism thinking mode of rationalism or irrationalism in history, which provides us with a new perspective to understand the nature of rationality from the resource, quantitative, and dynamic development views. In the sense of value rationality, bounded rationality is defective, but in the sense of instrumental rationality, bounded rationality is reasonable, so finding a proper balance point between them is necessary.

    The concept of bounded rationality in psychology and its extensive influence have led to another human rational evolution after the “probability revolution” of the Renaissance. It is one of the most important contributions made by this discipline to the treasure house of human thought and knowledge. It not only has far-reaching historical significance but also has interdisciplinary methodological significance.

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    Reports of Empirical Studies
    The impact of temporal and spatial consistency of audiovisual stimuli on Pip-and-Pop effect
    TANG Xiaoyu, CUI Xinzhong, GAO Min, YUAN Mengying
    2022, 54 (11):  1310-1324.  doi: 10.3724/SP.J.1041.2022.01310
    Abstract ( 1889 )   HTML ( 102 )  
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    Previous studies usually used the dynamic visual search paradigm to explore the Pip-and-Pop effect, which suggests that the Pip-and-Pop effect is influenced by multiple factors. But the impact of temporal and spatial consistency of audiovisual stimuli on the Pip-and-Pop effect is still controversial. In the present study, we applied the eye movement technology to the dynamic visual search paradigm to systematically investigate the impact of temporal and spatial consistency of audiovisual stimuli on the Pip-and-Pop effect. Based on the results of previous studies, we expected that the spatial and temporal consistency of audiovisual modulated the Pip-and-Pop effect. The more consistent the spatial location of audiovisual stimuli are, the greater the Pip-and-Pop effect will be. The more consistent the temporal audiovisual stimuli are, the greater the Pip-and-Pop effect will be.

    Experiment 1 was a 3 (set sizes: 36, 48, 60) × 4 (spatial consistency conditions: ipsilateral, contralateral, bilateral, no sound) within-subjects design, recruited 24 participants (5 males; age range: 19~28 years; mean age: 22.5 ± 2.3 years). The visual search displays consisted of 24, 36, or 48 red (13.9 cd/m2) or green (46.4 cd/m2) line segments (0.57°×0.17°) on a black (0.4 cd/m2) background. The auditory stimulus was 1000 Hz pure tone (65 dB, 60 ms, including 5 ms fade-in and 5 ms fade-out time), presented through speakers on the left and right sides behind the screen. Each trial started with a drift calibration point. The drift calibration point would not disappear until the participant gazed upon this point. This was followed by a central fixation point of 1000ms, and finally a search screen. The participants were required to find the target line segment and judge whether the target line segment was vertical or horizontal by pressing the key (Z key or M key) as quickly and accurately as possible. Experiment 2 was a 2 (set sizes: 36, 60) × 6 (temporal consistency conditions: -200 ms, -100 ms, 0 ms, 100 ms, 200 ms, no sound) within-subjects design, recruited 27 participants (5 males; age range: 18~25 years; mean age: 20.7 ± 2.4 years). These temporal consistency conditions represent the tone sounded before (-200, -100 ms), simultaneous with (0 ms), or after (100, 200 ms) the visual target event. The tone could also be absent (no sound). The experimental materials and procedures of Experiment 2 were identical to those in Experiment1.

    Regarding the results in Experiment 1, compared with the baseline condition (no sound), the search response time was the shortest under the condition of ipsilateral, the mean fixation number was the least, and the mean saccade amplitude was the smallest, indicating that the search efficiency was the highest in the ipsilateral condition, the Pip-and-Pop effect was the largest in the ipsilateral condition. The bilateral condition was the second. The contralateral condition showed no significant difference in the above indicators compared with the no sound condition, indicating that no Pip-and-Pop effect was found in the contralateral condition. The results showed that the more consistent the spatial location of audiovisual stimuli were, the greater the Pip-and-Pop effect was. In Experiment 2, compared with the no sound condition, we found that the response time of the search was significantly shorter, the mean fixation number in search decreased, the mean saccade amplitude increased, and the mean fixation duration became longer under the conditions of 0 ms, -100 ms and 100 ms. Compared with the no sound condition, conditions -200 ms and 200 ms showed no significant difference in the above indicators. This indicated that the conditions of 0 ms, -100 ms and 100 ms produced the Pip-and-Pop effect, and the Pip-and-Pop effect was the largest under the condition of 0ms, while the Pip-and-Pop effect did not find under the condition of -200 ms and 200 ms. The results showed that the more consistent the temporal audiovisual stimuli were, the greater the Pip-and-Pop effect was.

    In summary, the results showed that the more consistent the audiovisual stimuli were in space and time, the larger the Pip-and-Pop effect was. Therefore, the findings in the present study suggest that the temporal and spatial consistency of audiovisual stimuli modulates the Pip-and-Pop effect. The results provide evidence that the reason for the Pip-and-Pop effect is multisensory integration.

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    Target decision or action?The role of action in the attentional boost effect
    ZHENG Siqi, MENG Yingfang, HUANG Fajie
    2022, 54 (11):  1325-1339.  doi: 10.3724/SP.J.1041.2022.01325
    Abstract ( 2547 )   HTML ( 199 )  
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    The attentional boost effect (ABE) represents a phenomenon in which, in some dual tasks, increasing attention to a brief target in a detection task can enhance memory for unrelated items that are presented at the same time (relative to distractor-paired items). The ABE was different from the dual-task interference phenomenon found in previous studies, and to explain the ABE, Swallow and Jiang proposed a dual-task interaction model. This model claimed that the ABE was mainly triggered by the decision that an item is a target, which can lead to the transient but widespread perceptual enhancement of information by inducing a temporal selection mechanism. However, in ABE studies, the target detection tasks always coincide with Go responses that require action. One recent study found that action can enhance memory for unrelated items, which was called action-induced memory enhancement (AIME). Therefore, it is unclear whether the ABE is induced by the action or the target decision. To address this question, in the present study, the verbal paradigm of the ABE was modified and designed with a NoGo-target detection condition (NoGo-targets vs. Go-distractors) to separate target items from action responses, and a traditional Go-target detection condition (Go-targets vs. NoGo-distractors) was used for comparison. If the ABE is mainly triggered by the target decision, then NoGo-target detection could trigger the cross-conditional ABE (relative to NoGo-distractor items). In contrast, if the ABE is mainly triggered by the action, the NoGo-target items will not have any memory advantage.

    The present study included four experiments, and 137 valid data points were collected, including 33 valid data points in Experiment 1, 35 valid data points in Experiment 2, 36 valid data points in Experiment 3, and 33 valid data points in Experiment 4. The only difference among the four experiments was that the ratio of target-to-distractor items was different during the dual-task encoding phase. In Experiment 1, the ratio of target-to-distractor items was the same as that in the classic ABE verbal paradigm (1:5) to explore the role of AIME in the ABE. In Experiments 2 and 3, the ratio of target-to-distractor items was set to 1:1 and 1:2 to explore the role of the AIME and target decision in the ABE with different action frequencies. In Experiment 4, blank words (words without detection stimuli) were added in the detection phase to separate the action frequency (2/3) from the target frequency (relative to distractors; Go-targets: 4/5; NoGo-targets: 1/5) and verify the dynamic trade-off model of the target decision and action reaction proposed in the present study. Each experiment contained two conditions, namely, NoGo-target detection and Go-target detection, and each condition consisted of two phases, namely, a dual-task encoding phase and a recognition phase. During the dual-task encoding phase, a series of memory stimuli (words) and detection stimuli (coloured circles presented, 1 cm below the words) were presented at the same time, and the participants were asked to simultaneously perform the memory and detection tasks. During the recognition phase, only memory stimuli were presented, and the participants were required to judge the stimuli as old or new. The only difference between the NoGo-target condition and Go-target condition was reflected in the instructions for the detection task: in the Go-target condition, the participants were asked to press the space bar as quickly as possible when they saw the target circles (e.g., a red circle with Go-response) but did not need to respond when they saw other-coloured circles (i.e., distractor circles with NoGo-responses); in contrast, in the NoGo-target condition, the participants were required to press the space bar as quickly as possible for all circles (i.e., distractor circles with Go-responses) but withhold a button press for the target circle (e.g., a red circle with NoGo-response).

    The results showed that NoGo-target detection enhanced memory performance for target items (relative to Go-distractor/NoGo-distractor items) in the four experiments. First, it was found that the NoGo-target items were better remembered than the Go-distractor items and NoGo-distractor items in Experiment 1 (1:5 ratio), and performance with the Go-distractor items was worse than that with the NoGo-distractor items, showing that the ABE was triggered by the target decision without an action response and that actions had inhibitory effects at high frequencies. Second, it was found that the NoGo-target items were better recognized than the NoGo-distractor items but not better than the Go-distractor items in Experiment 2 (1:1 ratio), and the AIME was found with the Go-distractor items, showing that the boosting effect from the target decision on background information is robust, but the AIME affected the generation of the ABE within the NoGo-target condition. Third, it was found that NoGo-target items were better remembered than Go-distractor items and NoGo-distractor items in Experiment 3 (1:2 ratio), and there was no difference in memory performance between the Go-distractor items and the NoGo-distractor items, indicating that action frequency affected the generation of the ABE by adjusting the AIME. Finally, it was found that at 2/3 of the action frequency, both the Go-target detection with high target frequency and the NoGo-target detection with low target frequency triggered the ABE, and the memory performance was similar between the Go-distractor items and the NoGo-distractor items, indicating again that action frequency affected the generation of the ABE by adjusting the AIME, verifying the hypothesis of the dynamic trade-off model.

    Overall, the results of all four experiments found memory advantages with the NoGo-target items, but the generation of the ABE was affected by the frequency of action responses, indicating that the boosting effect from the target decision is robust in the ABE, and the action and the target decision work together in the generation of the ABE. Accordingly, we propose the dynamic trade-off model, arguing that the AIME at different frequencies dynamically trade-off against the boosting effect of target decisions and thus influence the ABE.

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    The effect of cognitive flexibility on probabilistic category learning
    FENG Xia, FENG Chengzhi
    2022, 54 (11):  1340-1353.  doi: 10.3724/SP.J.1041.2022.01340
    Abstract ( 2462 )   HTML ( 194 )  
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    Cognitive flexibility is related to one’s level of cognitive ability and creativity, and is an important feature of intelligence. With regard to probabilistic cue learning, whether the level of cognitive flexibility has an impact on the learning process in young adults remains to be studied. We addressed these questions by taking advantage of the event-related potentials (ERP) technique in two rule tasks with the same probability properties, which aimed to see how learners' cognitive flexibility promotes the dynamic process of probabilistic category learning, and its underlying neural mechanisms.

    We chose the “number-letter task” as the effective tool to assess learners’ cognitive flexibility level based on previous research and pilot testing. The participants were ranked according to their switch cost. The first 27% (smaller switch cost) were assigned to the high flexibility group, and the last 27% were assigned to the low group. All participants completed the picture selection task and the coin search task in the EEG environment on two occasions with a two week interval in between. The two tasks had the same probability pairs (0-1/3, 0-2/3, 1/3-2/3, 1-1/3), yet were different in form. Leaning curves for different groups, accuracy, latency, and ERPs at different learning stages were recorded and analyzed for each task.

    Behavioral results showed that in these two tasks, learners with high flexibility had a higher rule acquisition rate, although the high and low groups did not show any difference in rule acquisition speed. Learners' cognitive flexibility had cross-task advantages in probabilistic cue rule learning. For the ERP results, in the picture selection task there was a marginally significant difference between the two groups in the amplitude of the P300 component under the condition of preacquisiton-high - probability-reward. The advantage of high flexibility in rule learning was mainly due to the higher efficiency of feedback learning. In the coin search task, there was a significant difference between high and low flexibility groups in the amplitude of the FRN component under the conditions of preacquisiton- expectation and the conditions of postacquisition -unexpectation. Furthermore, only the low flexibility group showed a significant difference between the high and low probability conditions in the amplitude of the P300 component.

    In conclusion, the study suggests that learners with high cognitive flexibility have a cross-task advantage in probabilistic category learning, which is mainly due to more efficient feedback learning.

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    Different mechanisms for head and non-head words in the lexical boost effect on syntactic priming
    HUANG Jian, YANG Ziyu, HONG Danping, LIU Xiqin, WANG Suiping
    2022, 54 (11):  1354-1365.  doi: 10.3724/SP.J.1041.2022.01354
    Abstract ( 1472 )   HTML ( 131 )  
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    Lexical boost means that syntactic priming is enhanced by the lexical repetition between prime and target. It remains controversial whether the repetition of head words and that of non-head words induce similar boost effects. Two important theories in syntactic priming, the residual activation theory and the implicit learning theory, have quite different interpretations and predictions. The former holds that only the head word repetition can induce a lexical boost, while the latter holds that the non-head word repetition can induce a lexical boost of the same magnitude as the head word repetition does. There are conflicting experimental results on whether head and non-head word repetitions have similar lexical boost effects.

    We believe that one possible reason for the conflicting results in previous studies is that they lack sufficient power of the statistical test due to relatively small sample sizes. The present study explores the controversial issue by conducting three syntactic priming experiments of Mandarin double object (Experiments 1 and 3) and prepositional object (Experiment 2) structures, with a larger sample (115 participants each experiment) than that in previous research. To identify any possible difference in lexical boost effect, we manipulated the repetition of head constituents (i.e. verbs) and non-head constituents (i.e. argument nouns for agent, recipient, and theme) across prime and target.

    In all three experiments, we found that the lexical boost effect induced by the head word repetition was steady. The effect induced by the head word repetition was significantly stronger than that induced by the non-head word repetition. This indicates that the head constituent, rather than non-heads, plays a key role in the lexical boost. In addition, we found that the overlap of the direct object as a non-head induced a steady effect of lexical boost (although the effect is relatively weak). In Experiment 3, the subject repetition also induced a lexical boost effect. To some extent, these results seem to support the implicit learning theory since memory does play a certain role in lexical boost.

    The head word repetition and the non-head word repetition may reflect different cognitive mechanisms. We’d like to propose a new framework to interpret the lexical boost, which attempts to include both the residual activation theory and the implicit learning theory.

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    Container metaphor, intergroup attitude, and helping tendency toward domestic and foreign ethnic groups of Tibetan students in hinterland senior high school
    MENG Le, YE Can, WANG Jijia, ZHANG Jijia
    2022, 54 (11):  1366-1380.  doi: 10.3724/SP.J.1041.2022.01366
    Abstract ( 1791 )   HTML ( 131 )  
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    As a common ingroup, the Chinese nation community has unique characteristics. First, its properties are complex. Second, as an entity, it has various components. However, previous studies focused more on macro analysis, theoretical generalizations, and policy interpretations and less on microscopic arguments and empirical studies. Therefore, an empirical study on the identity of the Chinese nation community must be carried out. This study employs senior high school students who grew up in Tibetan areas and are current hinterland senior high school students to participate in three experiments. The most special characteristic of Tibetan students is their experiences on cross-ethnic communication and cross-cultural life.

    In Experiment 1, 50 Tibetan students in hinterland senior high school were employed as subjects. The relationship of the container and the community for the Chinese nation was investigated through the Spatial Stroop Paradigm. In Experiment 2, 50 Tibetan students were also employed as subjects. The Emotional Stroop Paradigm was used to explore the attitude of Tibetan students toward domestic and foreign ethnic groups. In Experiment 3, 320 Tibetan students were employed. Situational tasks of Money Helps and Time Helps were used to test the willingness to help someone from the domestic ethnic group or foreign ethnic group.

    Experiment 1 exhibited that the reaction time was significantly shorter when a domestic name appeared in the circle or a foreign name appeared outside the circle, which revealed that Tibetan students constructed the community for the Chinese nation as a container, placed the domestic ethnic groups in the container, and placed the foreign ethnic groups outside the container. Experiment 2 unveiled that the judgment reaction time of the positive target word was significantly shorter when the prime word was a domestic ethnic group name, and the judgment reaction time of the negative target word was significantly shorter when the prime word was a foreign ethnic group name, indicating that Tibetan students preferred the domestic ethnic groups and prejudiced the foreign ethnic groups. Experiment 3 showed that Tibetan students donated more money and time to someone from the domestic ethnic group who needed help, signifying that Tibetan students in hinterland senior high school had a stronger willingness to help domestic ethnic groups.

    This study suggests that Tibetan students in hinterland senior high school with rich experience on cross-ethnic communication and cross-cultural life constructed the Community for the Chinese nation as a container, and placed domestic ethnic groups in the container. Conclusively, Tibetan students had varying attitudes and different levels of help willingness toward domestic and foreign ethnic groups.

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    Is older adult happier with more filial piety children? The role of filial responsibility expectation of older adult
    LI Xiying, JIN Yitong, LIU Jing, ZHANG Xingyu, PI Zhongling
    2022, 54 (11):  1381-1390.  doi: 10.3724/SP.J.1041.2022.01381
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    Filial piety is an essential variable influencing the intergenerational interaction in the context of Chinese culture. Filial piety is a model of China’s refined traditional culture which guides family interactions based on blood relationships. It is, therefore, a social moral and normative behavior standard. Filial piety plays a vital role in older adults’ lives. However, conclusions from previous studies concerning the relationship between filial responsibility expectation and older adults’ quality of life are not consistent. This is partly because the studies did not consider filial support behaviors from adult children and filial discrepancy.

    Few studies have investigated whether older adults’ filial responsibility expectations match filial support from children and the effects of filial discrepancy on their life satisfaction and loneliness. To bridge this gap, the present study aimed to test whether filial discrepancy affects older adults’ life satisfaction and loneliness using a quadratic polynomial regression with response surface analysis.

    Our results showed that older adults’ life satisfaction was higher when emotional expectation and support, as well as contact expectation and support matched compared with when these expectations and supports did not match. The slope of the matching line was significantly positive (β = 3.23, p < 0.001). Specifically, a good match between emotional expectation and support linearly increased life satisfaction. Life satisfaction was higher when contact expectation and support matched than when they did not match. Moreover, the slope of the matching line was significantly positive (β = 1.74, p = 0.010). Specifically, when the contact expectation and support matched, life satisfaction increased with the increase in these two variables. Notably, older adults’ high life satisfaction was associated with children’s high instrumental support, but not the instrumental expectation. It was found that when emotional expectation and emotional support were mismatched, older adults felt lonelier when the emotional expectation was higher than emotional support compared with when the emotional expectation was lower than emotional support. Low loneliness was associated with high contact support and information support. However, loneliness was not related to contact expectation, information expectation, instrumental expectation, or instrumental support.

    In summary, our study found significant differences in the impact of filial discrepancy on the positive indicator of happiness in older adults (life satisfaction) and the negative indicator (loneliness). For life satisfaction, matching emotional expectation and emotional support, as well as contact expectation and contact support, are critical factors which improve older adults’ life satisfaction. In terms of loneliness, higher emotional expectation compared with emotional support increases older adults’ loneliness.

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    Shared responsibility promotes the benefit of interactive decision-making in novices: A hyperscanning study
    CHENG Xiaojun, LIU Meihuan, PAN Yafeng
    2022, 54 (11):  1391-1402.  doi: 10.3724/SP.J.1041.2022.01391
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    Social interaction is ubiquitous. It is widely accepted that social interaction, such as social decision-making, can promote individual’s ability and performance (the so-called “interaction benefit”). For example, it was reported that individuals gained more when making a joint decision with conspecifics. Little is known, however, whether and how this interaction benefit during decision making can be biased by shared responsibility (i.e., sharing the results of joint decision-making) between the interacting agents.

    To address this question, the present study used the dot location estimation task (i.e., an adapted paradigm for social decision-making) and functional near-infrared spectroscopy (fNIRS) hyperscanning (i.e., the measurement of two or more brains simultaneously) technique to investigate the impact of shared responsibility on social decision making. A total number of 70 participants were recruited, forming 35 same-gender dyads. Each dyad included one “expert” and one “novice” (differentiated based on their performance during an initial estimation of dot locations). The fNIRS optodes were placed over prefrontal and right temporo-parietal regions, with 23 channels for each participant.

    Our results showed that, on the behavioral level, only the novice in a dyad benefited from interaction; also, compared to the non-shared-responsibility condition, novices obtained a higher level of interaction benefit in the shared-responsibility condition. The dyad tended to adopt a “equality strategy” (i.e., decision-making is based on both one’s own thought and the partner’s suggestion) when sharing responsibility. On the brain imaging level, interpersonal brain synchronization (IBS) within expert-novice dyads in the prefrontal and right temporo- parietal regions were detected during social decision-making. More importantly, novices showed stronger IBS in the frontal pole for the shared-responsibility condition (vs. non-shared-responsibility condition). The enhancement of frontal pole IBS positively predicted interaction benefit during social decision-making. Finally, both interaction benefit and frontal pole IBS were selectively correlated with differential performance between novices and experts during the initial estimation of dot locations.

    These results suggest that sharing the results of joint decision-making can promote the benefit of interactive decision-making in novices. Interpersonal synchronization of frontal poles might serve as a potential brain mechanism. These findings have implications for decision-making, social-cognitive processes, and clinical practice.

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    Validation and estimation of expert-defined Q-matrix with polytomous attribute
    QIN Chunying, YU Xiaofeng
    2022, 54 (11):  1403-1415.  doi: 10.3724/SP.J.1041.2022.01403
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    Cognitive diagnosis has recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Generally, entries in the Q-matrix of traditional cognitive diagnostic tests are binary (two levels, defined as 0 and 1). Polytomous attributes (multi-levels, defined as 0, 1, …), particularly those defined as part of the test development process, can provide additional diagnostic information. Compared to binary attributes, polytomous attributes can not only describe the student's knowledge profile, but can provide more extensive details.

    As we all know, Q-matrix impacts the accuracy of cognitive diagnostic assessment greatly. Research on the effect of parameter estimation and classification accuracy caused by the error in Q-matrix already existed, and it turned out that Q-matrix gotten from expert definition or experience was more easily subject to be affected by subjective factors, lead to a misspecified Q-matrix. Under this circumstance, it’s urgently needed to find more objective polytomous-attribute Q-matrix verification and inference methods.

    The present research proposes the verification and estimation of expert-defined polytomous attribute Q-matrix based on the polytomous deterministic inputs, noisy, ‘‘and’’ gate (p-DINA) model. We intend to extend the methods adapted to binary Q-matrix verification and estimation to polytomous attribute Q-matrix, and the proposed methods which can be used in different conditions are joint estimation and online estimation. Simulation results show that: the joint estimation algorithm can be applied to the Q-matrix validation which needs an initial Q-matrix defined by experts, the online estimation algorithm can be applied to online estimate the “new items” based on a certain number of “based items”. Under the various settings in the simulations, the two estimation algorithms can recover the correct polytomous-attribute Q-matrix at a high probability. Empirical study also indicates that the two proposed algorithms can be applied in Q-matrix validation or estimation for CDA with polytomous attributes.

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    Joint-cross-loading multimodal cognitive diagnostic modeling incorporating visual fixation counts
    ZHAN Peida
    2022, 54 (11):  1416-1423.  doi: 10.3724/SP.J.1041.2022.01416
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    Students’ observed behavior (e.g., learning behavior and problem-solving behavior) comprises of activities that represent complicated cognitive processes and latent conceptions that are frequently systematically related to one another. Cognitive characteristics such as cognitive styles and fluency may differ between students with the same cognitive/knowledge structure. However, practically all cognitive diagnosis models (CDMs) that merely assess item response accuracy (RA) data are currently incapable of estimating or inferring individual differences in cognitive traits. With advances in technology-enhanced assessments, it is now possible to capture multimodal data, such as outcome data (e.g., response accuracy), process data (e.g., response times (RTs), and biometric data (e.g., visual fixation counts (FCs)), automatically and simultaneously during the problem-solving activity. Multimodal data allows for precise cognitive structure diagnosis as well as comprehensive feedback on various cognitive characteristics.

    First, using joint analysis of RA, RT, and FC data as an example, this study elaborated three multimodal data analysis methods and models, including separate modeling (whose model is denoted as S-MCDM), joint- hierarchical modeling (whose model is denoted as H-MCDM) (Zhan et al., 2022), and joint-cross-loading modeling (whose model is denoted as C-MCDM). Following that, three C-MCDMs with distinct hypotheses were presented based on joint-cross-loading modeling, namely, the C-MCDM-θ, C-MCDM-D, and C-MCDM-C, respectively. Three C-MCDMs, in comparison to the H-MCDM, introduce two item-level weight parameters (i.e., φi and λi) into the RT and FC measurement models, respectively, to quantify the impact of latent ability or latent attributes on RT and FC. The Markov Chain Monte Carlo method was used to estimate model parameters using a full Bayesian approach. To illustrate the three proposed models’ application and compare them to the S-MCDM and H-MCDM, multimodal data for a real-world mathematics test was used. Data was gathered at a prominent university on the East Coast of the United States in an eye-tracking lab. An I = 10 mathematics items test was given to N = 93 university students with normal or corrected vision. The test included K = 4 attributes, and the related Q-matrix is shown in Figure 3. The data is divided into three modalities: RA, RT, and FC, which were all collected at the same time. The data was fitted to all five multimodal models.

    In addition, two simulation studies were conducted further to explore the psychometric performance of the proposed models. The purpose of simulation study 1 was to explore whether the parameter estimates of the proposed models can converge effectively and explore the recovery of parameter estimation under different simulated test situations. The purpose of simulation study 2 was to explore the relative merits of C-MCDMs and H-MCDM, that is, to explore the necessity of considering cross-loading in multimodal data analysis.

    The results of the empirical study showed that (1) the C-MCDM-θ has the best model-data fitting, followed by the H-MCDM and the S-MCDM. Although the DIC showed that the C-MCDM-D and C-MCDM-C also fitted the data well, the results were only for reference because some parameter estimates in these two models did not converge; that (2) the correlation coefficients between latent ability and latent processing speed and that between latent ability and latent concentration were weak, making it difficult to fully exploit the theoretical advantages of H-MCDM over S-MCDM (Ranger, 2013). By contrast, since the C-MCDM-θ can directly utilize the information from RT and FC data, the standard error of the estimates of its latent ability was significantly lower than that of the previous two competing models; and that (3) the median of the estimates of φi was less than 0, which indicated that for most items, the higher the participant’s latent ability is, the longer the time it will take to solve the items; and the median of the estimates of λi was higher than 0, which indicated that for most items, the higher the participant’s latent ability is, the more number of fixation counts he/she shown in problem-solving. Furthermore, it should be noted that the estimates of φi and λi do not always have the same sign for different items, indicating that the influence of latent abilities on RT and FC has different directions (i.e., facilitation or inhibition) for different items. Furthermore, simulation study 1 indicated that the parameter estimation of the proposed three models could converge effectively and the recovery of model parameters was good under different simulated test situations. The results of simulation study 2 indicated that the adverse effects of ignoring the possible cross- loadings are more severe than redundantly considering the cross-loadings.

    Overall, the results of this study indicate that (1) fusion analysis is more suitable for multimodal data that provides parallel information than separate analysis; that (2) through cross-loading, the proposed models can directly use information from RT and FC data to improve the parameter estimation accuracy of latent ability or latent attributes; that (3) the results of the proposed models can be used to diagnose cognitive structure and infer other cognitive characteristics such as cognitive styles and fluency; and that (4) the proposed models have better compatibility with different test situations than H-MCDM.

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