# Effects of Exogenous and Endogenous Attention on Metacontrast Masking

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Apparatus

#### 2.3. Stimuli and Procedures

^{2}) screen. After a random delay (500–1000 ms), a black pre-cue (an arrow at the center in the endogenous attention blocks, or a 0.3 deg square at 3.0 deg eccentricity in the exogenous attention blocks) was shown for 50 ms, indicating the target location. After a variable CTOA, an array of six (endogenous) or four (exogenous) oriented bars (1 deg long, 0.1 deg wide) was presented for 10 ms around an imaginary circle centered on the fixation point, so that all bars had the same retinal eccentricity. In the exogenous attention blocks, we had 4 oriented bars and the eccentricity of each bar was 5 deg. In the endogenous attention condition, we had 6 oriented bars. We increased the eccentricity for each bar to 6 deg so that the bars would not be too close to each other.

#### 2.4. Avoiding Floor and Ceiling Effects

#### 2.5. Statistical Analyses and Modelling

#### 2.5.1. Performance Measures

#### 2.5.2. Data analyses

**Analysis (1) Avoiding floor and ceiling effects:**For the first analysis, the goal was to establish that floor and ceiling effects are indeed avoided. For this purpose, we ran a power analysis to determine the number of trials per SOA at 0.7 power level based on the data from pilot experiments and our previous studies on metacontrast masking. Note that this value does not reflect the overall power of our other two analyses described below, nor the power of across-observers tests. It is merely used as an objective criterion to set a priori the number of trials per observer. This analysis yielded around 200 trials in total for baseline (i.e., no mask condition) and masking conditions. Hence, each observer (except GQ who ran 70 trials for both conditions) ran 100 trials per SOA for both masking and baseline conditions. Table 1 lists the target and mask luminances, as well as the results of t-tests used to check whether or not both criteria listed above were met, for all observers. In general, p-values indicate highly significant differences from ceiling and floor levels, indicating that floor and ceiling effects are avoided.

**Analysis (2) Assessing attention metacontrast interactions by analyzing masking functions:**The second analysis was directed to masking functions with the goal of determining whether attention and metacontrast interact. Because we used different stimulus parameters for each observer for the reasons mentioned above, we adopted a within-observer analysis approach and analyzed transformed-performance of each observer separately. We fitted a series of linear and polynomial embedded regression models listed in Table 2 to determine the contributions of the main factors (e.g., CTOA, SOA) and their interactions. In the exogenous attention condition, only the trials where the peripheral cue correctly indicated the target location (i.e., valid trials) were included in the analyses. The results of the invalid trials in the exogenous attention condition were analyzed separately and included in Appendix A.

^{2}metrics in the selection of best performing model. Model selection results were similar, if not identical, with both metrics for all observers. Both metrics penalize models for the number of free parameters. In addition, the BIC approach provides comparisons between different models in terms of their likelihood. To compare models, one needs to look at differences between BICs from different models. A BIC difference of x between model A and model B (i.e., BIC

_{A}−BIC

_{B}) corresponds to e

^{−x}-to-1 odds favoring model A. Therefore, the regression model with the smallest BIC value is the most likely model compared to others, and the BIC difference between two models indicate their relative likelihood.

**Analysis (3) Statistical mixture modeling of data:**Statistical mixture models have a long history in behavioral, perceptual, and cognitive studies. In several studies, it was noted that a mixture of statistical models (e.g., combined Gaussian and Uniform distributions) provide a better account of data compared to a single one (e.g., Gaussian), even when the difference in the number of parameters is taken into account. Mixture models have been used in modeling VSTM [14,59,60,61], visual encoding [14,60], crowding [62,63], and masking [64,65]. An upshot of this approach is that it can provide a meaningful interpretation for the parameters of the model. For example, as discussed below, for a Gaussian + Uniform mixture model, the mean and variance of the Gaussian can be interpreted as the accuracy and precision of the underlying process, respectively, whereas the weight of the Uniform component can be interpreted as the guess rate.

_{max}(${m}_{j}$) = max(L(${m}_{j}$|θ)). We used the Riemann-sum approximation to compute Equation (2) and we had at least 50 bins in each parameter dimension. The difference between the BMC values from two different models is equivalent to the logarithm of their likelihood ratios. Therefore, a model with larger BMC performs better. A BMC difference of x between model A and model B corresponds to e

^{x}-to-1 odds favoring model A.

**Analysis (4) Analysis of winning statistical model’s parameters:**Analysis 2 is conducted for determining whether attention and metacontrast interact. Analysis 3 provides a parametric interpretation of the data. We investigated the relationship between masking strength and model parameters by computing the correlation (Pearson R coefficients) between masking functions and the model parameters. The masking function is a plot of target visibility as a function of target-mask SOA. A strong correlation would suggest a critical role for that model parameter in accounting for masking effects, and a change in correlation with CTOA would suggest an interaction between attention and masking for that parameter (or for the process represented by that parameter).

## 3. Predictions

## 4. Results

_{2,10}= 8.060; p = 0.008; η

_{p}

^{2}= 0.617). Although there was an increasing trend in performance with CTOA, a paired t-test between performance at zero CTOA and ~100 ms CTOA in the exogenous attention condition was only marginally significant (t(5) = 2.451; p = 0.058).

#### Statistical Mixture Modeling

^{5}-to-1, 6.7-to-1, and 30.0-to-1 odds, in favor of the GU model, and suggest a “decisive evidence” favoring the GU model [72]. Similarly, in the exogenous attention condition, the BMC of the GU model was 14.3, 2.1, and 3.2 larger than that of the G, GUCA, and GUNN models, respectively. These BMC differences correspond to 1.6 × 10

^{6}-to-1, 8.2-to-1, and 24.5-to-1 odds, all favoring the GU model. Next, we analyzed the model parameters of the GU model to determine whether any interaction between metacontrast masking and attention exists. Since the Gaussian and the Uniform components in the GU model are interpreted to represent different processes (stimulus encoding and guessing), examination of model parameters has the potential to tease apart different relationships between these processes, metacontrast, and attention.

^{2}xCTOA interaction terms (see Table 2 for a complete list of all regression models). In the exogenous attention condition, the best regression model for the weight of the Uniform term was M16 for three out of six observers. Here, the best model for observer FG was again M21. However, for observer EB, there was no interaction between SOA and CTOA in the exogenous attention condition. Moreover, for observers MNA and SA, the best regression models were M20 and M21, respectively. Both M20 and M21 contain a quadratic SOA and CTOA interaction, which suggest a masking strength-dependent effect of attention. This is apparent in the nonuniform, SOA-dependent drops in the weight parameter with an increase in CTOA for these observers (Figure 6B, U

_{weight}). Interestingly, we did not find such interactions for the weight parameter in the endogenous attention condition, as well as the transformed performance in both attention conditions.

## 5. Discussion

#### 5.1. Implications for Models of Attention

^{2}and CTOA. As revealed by statistical modeling of the distribution of signed response-errors, rather than just the mean magnitude of errors, the interaction between SOA

^{2}and CTOA was evident in the frequency of random guessing behavior for two observers in the endogenous attention condition, and for three observers in the exogenous attention condition. In sum, although the underlying neurophysiological mechanism is unspecified at this time, our finding that there might be modest interactions between metacontrast masking and attention can be explained by PTM. However, as mentioned above, this explanation rests on some unspecified mechanism, according to which the metacontrast mask adds external noise in an SOA-dependent manner.

#### 5.2. Implications for Masking Models

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**The transformed performance as a function of SOA for invalid trials in the exogenous attention condition for all CTOAs. The horizontal axes represent SOA and the vertical axes represent transformed performance. Red color represents zero CTOA and blue color represents positive CTOA value (ranging from 80 to 120). The dotted horizontal lines indicate baseline performance. The markers and the dashed lines represent empirical data whereas the solid lines show the best-fit regression model. Each panel shows data from a single observer. The best regression model (see Table 2) is given on top of each panel. Error bars represent ±SEM across trials (n = 100).

**Figure A2.**The transformed performance as a function of SOA for invalid trials in the exogenous attention condition for all CTOAs. The horizontal axes represent SOA and the vertical axes represent transformed performance. Red color represents zero CTOA and blue color represents positive CTOA value (ranging from 80 to 120). The dotted horizontal lines indicate baseline performance. The markers and the dashed lines represent empirical data whereas the solid lines show the best-fit regression model. Each panel shows data from a single observer. The best regression model (see Table 2) is given on top of each panel. Error bars represent ± SEM across trials (n = 100).

## Appendix B

^{2}values for the best-fitting models for all observers and experiments.

**Table A1.**A summary the R

^{2}(and Adjusted R

^{2}) values for the best fitting models for all observers and experiments.

ATB | EB | FG | GQ | MNA | SA | |
---|---|---|---|---|---|---|

Endogenous | 0.82 (0.74) | 0.97 (0.95) | 0.96 (0.93) | 0.90 (0.87) | 0.81 (0.75) | 0.89 (0.85) |

Exogenous | 0.84 (0.73) | 0.90 (0.81) | 0.75 (0.54) | 0.94 (0.90) | 0.85 (0.76) | 0.91 (0.85) |

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**Figure 1.**The stimulus sequences for both the endogenous (

**top**) and exogenous (

**bottom**) attention conditions.

**Figure 2.**(

**A**) The time courses of effects of exogenous (solid line) and endogenous (dashed line) cueing [68]. The blue and red arrows indicate endogenous and exogenous cues, respectively. (

**B**) The predicted outcomes assuming no interaction between attention and masking. (

**C**,

**D**) Possible outcomes that would indicate interactions between metacontrast and attention.

**Figure 3.**The transformed performance in the (

**A**) endogenous and (

**B**) exogenous attention conditions for all CTOAs and SOAs. The horizontal axes represent SOA and the vertical axes represent transformed performance (see Methods, Section 2). Different colors represent different CTOA conditions. The dotted horizontal lines indicate baseline (i.e., without masks) performance. The markers and the dashed lines represent empirical data, whereas the solid lines show the best-fit regression model. Each panel shows data from a single observer. The initials of each observer and the best regression model (see Table 2) are given on top of each panel. Error bars represent ± SEM across trials (n = 100). Note that only the validly cued trials are included in both conditions, which correspond to 100% and 25% of the trials in the endogenous and exogenous attention conditions, respectively. Results of invalidly cued trials in exogenous attention condition is shown in Appendix A. (

**C**) The baseline performance (averaged across observers) as a function of CTOA in both conditions. Error bars represent ± SEM across observers (n = 6).

**Figure 4.**The Bayesian Information Criterion (BIC) differences between each pair of the regression models listed in Table 2. (

**A**) Endogenous attention condition. (

**B**) Exogenous attention condition. Greenish colors represent equivalent model performance whereas blue and red colors represent better and worse model performance, respectively, in comparing the model listed on the y axis to the model listed on the x axis.

**Figure 5.**Pairwise Bayesian Model Comparison (BMC) differences between the statistical models tested. A square with coordinates (x,y) on each plot represents the BMC difference between model y and x. In order to have the same color notation (i.e., cooler colors mean better model performance and hotter colors mean worse model performance) as in Figure 4, we flipped the sign of the BMC differences. For both types of attention and for all observers, the GU model performs best in explaining the distribution of signed response errors, as indicated by the darkest blue color at the (G, GU) coordinate in all panels.

**Figure 6.**Pairwise BMC differences between the statistical models tested. A square with coordinates (x,y) on each plot represents the BMC difference between model y and x. In order to have the same color notation (i.e., cooler colors mean better model performance and hotter colors mean worse model performance) as in Figure 4, we flipped the sign of the BMC differences. For both types of attention and for all observers, the GU model performs best in explaining the distribution of signed response errors, as indicated by the darkest blue color at the (G, GU) coordinate in all panels.

**Figure 7.**The correlations between masking functions and the GU model parameters for the (

**A**) endogenous, and (

**B**) exogenous attention conditions. The top row represents the standard deviation of the Gaussian whereas the bottom row represents the weight of the Uniform.

**Table 1.**The target, mask, and cue luminance values in cd/m

^{2}(and corresponding Weber contrast values) are listed for each observer in endogenous and exogenous attention conditions. The background luminance was 60 cd/m

^{2}for all observers. The results of t-tests used to assess whether criteria C1 and C2 are met are also listed for each observer. Note that we used two-sample t-tests with unequal variances for testing for criterion C1, and one-sample t-tests against chance level (0.5) for testing for criterion C2.

Endogenous | |||||

Luminance (Contrast) | Statistical Criteria | ||||

Observer | Target | Mask | Cue | C1 (Ceiling) | C2 (Floor) |

ATB | 43 (−0.28) | 15 (−0.75) | 10 (−0.83) | t(150.7) = −2.18; p = 0.016 | t(99) = 4.11; p < 0.001 |

EB | 12.5 (−0.79) | 30 (−0.5) | 10 (−0.83) | t(164.8) = −2.22; p = 0.014 | t(99) = 6.15; p < 0.001 |

FG | 46 (−0.23) | 18 (−0.7) | 10 (−0.83) | t(145.5) = −2.73; p = 0.004 | t(99) = 8.27; p < 0.001 |

GQ | 46 (−0.23) | 0 (−1) | 10 (−0.83) | t(141.6) = −2.53; p = 0.006 | t(99) = 3.92; p < 0.001 |

MNA | 42 (−0.3) | 20 (−0.67) | 10 (−0.83) | t(142.6) = −2.19; p = 0.015 | t(99) = 5.86; p < 0.001 |

SA | 47 (−0.22) | 18 (−0.7) | 10 (−0.83) | t(138.6) = −2.94; p = 0.002 | t(99) = 7.72; p < 0.001 |

Exogenous | |||||

Luminance (Contrast) | Statistical Criteria | ||||

Observer | Target | Mask | Cue | C1 (Ceiling) | C2 (Floor) |

ATB | 44 (−0.27) | 10 (−0.83) | 30 (−0.5) | t(167.7) = −2.23; p = 0.013 | t(99) = 6.26; p < 0.001 |

EB | 40.5 (−0.32) | 12 (−0.8) | 30 (−0.5) | t(181.5) = −1.87; p = 0.031 | t(99) = 5.24; p < 0.001 |

FG | 46 (−0.23) | 18 (−0.7) | 30 (−0.5) | t(180.6) = −2.5; p = 0.007 | t(99) = 6.26; p < 0.001 |

GQ | 46.5 (−0.22) | 6 (−0.9) | 30 (−0.5) | t(125.3) = −2.9; p = 0.002 | t(69) = 4.34; p < 0.001 |

MNA | 43.5 (−0.28) | 30 (−0.5) | 30 (−0.5) | t(137) = −2.34; p = 0.01 | t(99) = 6.68; p < 0.001 |

SA | 48 (−0.2) | 30 (−0.5) | 30 (−0.5) | t(134.6) = −3.81; p < 0.001 | t(99) = 3.73; p < 0.001 |

**Table 2.**The regression models used to fit transformed performances and the winning model parameters are listed. The models are sorted based on number of parameters. The models M1, M2, M3, M4, M7, M8, M9, and M14 are the standard linear regression models whereas the remainder of models has quadratic main factors and/or interactions. τ represents SOA (Stimulus Onset Asynchrony) and n represents CTOA (cue-target onset asynchronies). β’s are the coefficients of the models and ε represents the error term.

ID | Regression Model |
---|---|

M1 | Y = β_{0} + ε |

M2 | Y = β_{0} + β_{1} τ + ε |

M3 | Y = β_{0} + β_{1} n + ε |

M4 | Y = β_{0} + β_{1} τ n + ε |

M5 | Y = β_{0} + β_{1} τ^{2} + ε |

M6 | Y = β_{0} + β_{1} τ^{2} n + ε |

M7 | Y = β_{0} + β_{1} τ + β_{2} n + ε |

M8 | Y = β_{0} + β_{1} τ + β_{2} τ n + ε |

M9 | Y = β_{0} + β_{1} n + β_{2} τ n + ε |

M10 | Y = β_{0} + β_{1} τ^{2} + β_{2} n + ε |

M11 | Y = β_{0} + β_{1} τ^{2} + β_{2} τ^{2} n + ε |

M12 | Y = β_{0} + β_{1} n + β_{2} τ^{2} n + ε |

M13 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + ε |

M14 | Y = β_{0} + β_{1} τ + β_{2} n + β_{3} τ n + ε |

M15 | Y = β_{0} + β_{1} τ^{2} + β_{2} n + β_{3} τ^{2} n + ε |

M16 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} n + ε |

M17 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} τ n + ε |

M18 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} τ^{2} n + ε |

M19 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} n + β_{4} τ n + ε |

M20 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} n + β_{4} τ^{2} n + ε |

M21 | Y = β_{0} + β_{1} τ + β_{2} τ^{2} + β_{3} n + β_{4} τ n + β_{5} τ^{2} n + ε |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Agaoglu, S.; Breitmeyer, B.; Ogmen, H.
Effects of Exogenous and Endogenous Attention on Metacontrast Masking. *Vision* **2018**, *2*, 39.
https://doi.org/10.3390/vision2040039

**AMA Style**

Agaoglu S, Breitmeyer B, Ogmen H.
Effects of Exogenous and Endogenous Attention on Metacontrast Masking. *Vision*. 2018; 2(4):39.
https://doi.org/10.3390/vision2040039

**Chicago/Turabian Style**

Agaoglu, Sevda, Bruno Breitmeyer, and Haluk Ogmen.
2018. "Effects of Exogenous and Endogenous Attention on Metacontrast Masking" *Vision* 2, no. 4: 39.
https://doi.org/10.3390/vision2040039