generalized linear models (glms) assuming binomial distributions and using the logit link function Search Results


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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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SAS institute proc logistic/ proc genmod version 9.3.1
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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SAS institute proc glimmix
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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RStudio rstudio version 1.3.1103
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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RStudio generalized linear model (glm) function
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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CH Instruments glm function
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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SAS institute proc corr
( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of <t>generalised</t> <t>linear</t> <t>model</t> <t>(GLM)</t> coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).
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( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of generalised linear model (GLM) coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).

Journal: eLife

Article Title: Clarifying the role of an unavailable distractor in human multiattribute choice

doi: 10.7554/eLife.83316

Figure Lengend Snippet: ( a ) Multiattribute stimuli in a previous study . Participants made a speeded choice between two available options (HV: high expected value; LV: low expected value) in the presence (ternary) or absence (binary) of a third distractor option (‘ D ’). Three example stimuli are labelled for illustration purposes only. In the experiment, D was surrounded by a purple square to show that it should not be chosen. ( b, c ) Relative choice accuracy (probability of H choice among all H and L choices) in ternary trials (panel b) and in binary-choice baselines (panel c) plotted as a function of both the expected value (EV) difference between the two available options (HV − LV) ( y -axis) and the EV difference between D and H ( x -axis). Relative choice accuracy increases when HV − LV increases (bottom to top) as well as when DV − HV increases (left to right, i.e., positive D effect). ( d–f ) Predicting relative accuracy in human data using regression models (Methods). Asterisks: significant effects [p < 0.05; two-sided one-sample t- tests of generalised linear model (GLM) coefficients against 0] following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant. ( g ) Rival hypotheses underlying the positive notional distractor effect on binary-choice accuracy. Left: EV indifference contour map; Right: additive utility (AU) indifference contour map. Utility remains constant across all points on the same indifference curve and increases across different curves in evenly spaced steps along the direction of the dashed grey line. Decision accuracy scales with Δ(utility) between H and L in binary choices. Left (hypothesis 1): Δ(EV) = (HV − LV)/(HV + LV) by virtue of divisive normalisation (DN); because HV 2 − LV 2 = HV 1 − LV 1 , and HV 2 + LV 2 > HV 1 + LV 1 , Δ(EV 2 ) becomes smaller than Δ(EV 1 ). Right (hypothesis 2): Δ(AU) = AU H − AU L ; Δ(AU 2 ) < Δ(AU 1 ) by virtue of additive integration. ( h, i ) Regression analysis of model-predicted accuracy in binary choice. EV + DN model corresponds to hypothesis 1 whilst AU model corresponds to hypothesis 2 in panel g. Error bars = ± standard error of the mean (SEM) ( N = 144 participants).

Article Snippet: We used logit binomial GLM to analyse trial-by-trial relative choice accuracy (Matlab’s glmfit with ‘binomial’ distribution and ‘logit’ link function).

Techniques:

The generalised linear models (GLMs) here included an additional regressor HV + LV. Error bars = ± standard error of the mean (SEM) ( N = 144 participants). Asterisks: significant effects (p < 0.05; two-sided one-sample t -tests of GLM beta coefficients against 0) following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant.

Journal: eLife

Article Title: Clarifying the role of an unavailable distractor in human multiattribute choice

doi: 10.7554/eLife.83316

Figure Lengend Snippet: The generalised linear models (GLMs) here included an additional regressor HV + LV. Error bars = ± standard error of the mean (SEM) ( N = 144 participants). Asterisks: significant effects (p < 0.05; two-sided one-sample t -tests of GLM beta coefficients against 0) following Holm’s sequential Bonferroni correction for multiple comparisons. n.s.: non-significant.

Article Snippet: We used logit binomial GLM to analyse trial-by-trial relative choice accuracy (Matlab’s glmfit with ‘binomial’ distribution and ‘logit’ link function).

Techniques: