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ABSTRACT For 50 years or so, visual search experiments have been used to examine how humans find behaviourally relevant objects in complex visual scenes. For the same length of time, there has been a dispute over whether this search is performed in a serial or parallel fashion.
In this paper, we approach this dispute by numerically fitting a serial search model and a parallel search model to reaction time (RT) distributions from three visual search experiments (feature search, conjunction search, spatial configuration search). In order to do so, we used a free-likelihood method based on a novel kernel density estimator (KDE). The serial search model was the Competitive Guided Search (CGS) model by Moran et al. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24–24. We were able to replicate the ability of CGS to model RT distributions from visual search experiments, and demonstrated that CGS generalizes well to new data. The parallel model was based on the biased-competition theory and utilized a very simple biologically-plausible winner-take-all (WTA) mechanism from Heinke and Humphreys’s (2003).
Attention, spatial representation and visual neglect: Simulating emergent attention and spatial memory in the Selective Attention for Identification Model (SAIM). Psychological Review, 110(1), 29–87. With this mechanism, SAIM has been able to explain a broad range of attentional phenomena but it was not specifically designed to model RT distributions in visual search. Nevertheless, the WTA was able to reproduce these distributions. However, a direct comparison of the two models suggested that the serial CGS is slightly better equipped to explain the RT distributions than the WTA mechanism. The CGS’s success was mainly down the usage of the Wald distribution which was specifically designed to model visual search.
Future WTA versions will have to find a biologically plausible mechanism to reproduce such a RT distribution. Finally, both models suffered from a failure to generalize across all display sizes. From these comparisons, we developed suggestions for improving the models and motivated empirical studies to devise a stronger test for the two types of searches. Visual search experiment The data used in this paper was collected as part of Lin et al.’s ( Lin, Y-S., Heinke, D., & Humphreys, G. Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework.
Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ) experiments. Details of the design can be found in Lin et al. ( Lin, Y-S., Heinke, D., & Humphreys, G. Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework.
Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ). The search displays were arranged in a circular layout (see ) in which items can be placed in 25 locations.
The display size was 3, 6, 12 or 18 items. Each condition comprised 100 trials. Three different search experiments were conducted: feature search, conjunction search, spatial configuration search. In the feature search task, the target was a dark square while the distractors were grey squares. In the conjunction search, participants looked for a vertical dark bar amongst two types of distractors, vertical grey bars and horizontal dark bars.
The spatial configuration task used two items, digit 2 (target) and digit 5 (distractor). Each search task was completed by 20 participants; one participant was removed from feature and conjunction search tasks due to high error rates. Shows the resulting search functions for the present condition. In addition, Lin et al. ( Lin, Y-S., Heinke, D., & Humphreys, G.
Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework. Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ) found that for feature search and conjunction search the RT distribution’s skewness increased with increasing display size. For spatial configuration search the relationship between skewness and display size was more complex. The skewness first increased over the smaller display sizes (3, 6, 12) but then decreased from 12 to 18. The results indicate that the data provides a good basis for testing the models on a range of search task difficulties similar to Wolfe et al.’s ( Wolfe, J.
M., Palmer, E. M., & Horowitz, T.
Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311. Doi: 10.1016/j.visres.2009.11.002, ) data. However, there is an interesting difference between their data and our data. In our study, participants made roughly twice as many as errors as in their experiments. This difference can be explained because in Wolfe et al.’s ( Wolfe, J.
M., Palmer, E. M., & Horowitz, T. Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311. Doi: 10.1016/j.visres.2009.11.002, ) experiments, participants completed all three tasks with 500 trials in each condition. In our study, participants completed only 100 trials per condition and not all tasks.
Thus, in Wolfe et al.’s ( Wolfe, J. M., Palmer, E. M., & Horowitz, T. Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311. Doi: 10.1016/j.visres.2009.11.002, ) study participants were highly practiced compared to our study.
When we re-analysed Wolfe et al.’s ( Wolfe, J. M., Palmer, E. M., & Horowitz, T. Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311.
Doi: 10.1016/j.visres.2009.11.002, ) data and included only the first 100 trials of each condition the error rates were similar to our error rate. Hence our dataset poses the interesting challenge to CGS whether CGS will also be able to model less practiced participants. SAIM’s winner-take-all model The biased competition model is based on SAIM’s WTA mechanism (Heinke & Backhaus, Heinke, D., & Backhaus, A. Modeling visual search with the Selective Attention for Identification model (VS-SAIM): A novel explanation for visual search asymmetries. Cognitive Computation, 3(1), 185– 205. Doi: 10.1007/s12559-010-9076-x,; Heinke & Humphreys, Heinke, D., & Humphreys, G.
Attention, spatial representation and visual neglect: Simulating emergent attention and spatial memory in the Selective Attention for Identification Model (SAIM). Psychological Review, 110(1), 29– 87.
Doi: 10.1037/0033-295X.110.1.29,; Zhao, Humphreys, & Heinke, Zhao, Y., Humphreys, G. W., & Heinke, D. A biased-competition approach to spatial cueing: Combining empirical studies and computational modelling.
Visual Cognition, 20(2), 170– 210. Doi: 10.105.2012.655806, ). This WTA mechanism uses a single layer of “neurons” which are connected by a lateral inhibition (see (a)).
If the correct parameters are chosen, the neuron with the highest input is activated while all other neurons are shut down (see (b) for an exemplar simulation result). In other words, all neurons compete with each other and the neuron with the largest input wins the competition. The mathematical description of the model as follows.
Where f( x) is a sigmoid function with parameters slope ( m) and intercept ( s), is the accumulation rate of input activation and w is the strength of the lateral inhibition, is Gaussian noise with the variance, is the input to the ith neuron, is the output activation of ith neuron, is the internal activation of the ith neuron. These equations are based on a mathematical description of neurophysiological processes using a spiking-rate neuron model. The Gaussian noise takes into account the randomness of neural processes.
The sigmoid function models the non-linear relationship between cell activation and output spiking rate. The differential equation models the leaky accumulation behaviour of synapses. The summation term realizes the lateral inhibition within the layer (inhibitory neuron).
To adapt the model to modelling visual search data, we made several simple assumptions. Each “neuron” is assumed to correspond to an item location in the search display. If a location is empty the input is set to zero. The neuron for the target location is set to one while the distractor neurons are set to a saliency value.
To model the reaction time, we introduced a decision boundary and computed the time it takes for a neuron to pass this threshold. If it is a distractor neuron the response is recorded as “target absent”; if it is a target neuron the response is “target present”. It is worth noting that SAIM-WTA is similar to the Leaky Competing Accumulation (LCA) model (Usher & McClelland, Usher, M., & McClelland, J.
The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review, 108(3), 550– 592. Doi: 10.1037/0033-295X.108.3.550, ). However, to the best of our knowledge, LCA has never been applied to visual search.
Moreover and similar to LCA, SAIM-WTA stands in the tradition of the Parallel Distributed Processing (PDP) framework (Rumelhart & McCleland, 1986) in that it draws on principles of neural information processing in order to understand phenomena at the behavioural level (see Mavritsaki, Heinke, Allen, Deco, & Humphreys, Mavritsaki, E., Heinke, D., Allen, H., Deco, G., & Humphreys, G. Bridging the gap between physiology and behavior: Evidence from the sSoTS model of human visual attention. Psychological Review, 118(1), 3– 41. Doi: 10.1037/a0021868, for a discussion of linking the neural level with the behavioural level through means of computational models). In addition, some mechanisms and conceptualizations are also similar to stochastic drift diffusion models (Busemeyer & Diederich, Busemeyer, J.
R., & Diederich, A. Cognitive modelling. Thousand Oaks, CA: Sage.; Ratcliff, Ratcliff, R. A theory of memory retrieval. Psychological Review, 85(2), 59– 108. Doi: 10.1037/0033-295X.85.2.59, ). These models assume that perceptual decision making is based on an accumulation of perceptual information.
Once this accumulation has reached a certain level (i.e., threshold) a decision is made (i.e., a response is generated). The time it takes for the accumulation to reach the threshold is interpreted as reaction time. SAIM-WTA can be framed in terms of these drift diffusion models in that SAIM-WTA’s model accumulates information about the search items (i.e., identifies them) and once this information has reached a certain level the model/participant initiates a corresponding response.
However, and different from drift diffusion models, the accumulators interfere with each other. SAIM-WTA has seven free parameters.
In explorations of the parameter space prior to work presented here, we found several regions where it was possible to achieve a similar quality of fit. Subsequently, we focused on a region where it was possible to reduce the number of free parameters to the smallest possible number (i.e., three) while still obtaining the best fits for all participants (see for the values of the fixed parameters). In addition, the remaining free parameters (accumulation rate, decision boundary, distractor saliency) allowed us to ask interesting theoretical questions about the factors which influence visual search performance. Given the biased-competition theory’s assumptions, we expect that the distractor saliency (target–distractor similarity) increases with task difficulty, but it is not clear if the distractor saliency is sufficient to explain the differences between the tasks or is there also a difference in terms of the difficulty of identifying items (as expressed by accumulation rate)?
In fact, computational models such as SAIM (and CGS) suggest the involvement of a separate object identification stage. Competitive Guided Search (CGS) Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) CGS implements a serial search based on Wolfe’s ( Wolfe, J. Guided search 4.0. Gray (Ed.), Integrated models of cognitive systems (cognitive models and architectures) (pp. Oxford: Integrated Models of Cognitive Systems.
) two stage architecture. The guidance through the saliency map is implemented through a probabilistic selection where target item has the probability to be selected: and the distractor items: is the saliency of the target relative to the distractor. If the target saliency is smaller than one there is no guidance; n is the number of items currently available for selection and is decremented after each search step.
Hence, CGS assumes that once an item is identified it is not revisited again. Prior to each search step, CGS decides whether to continue with the search, or to quit the search and decide that the target is absent.
The probability to quit is calculated in the following way: Again, n is decremented after each search. Hence, the probability to quit increases with each search step. This effect is increased further by modifying at each search step: Note that the value of is zero at the beginning of the search. At each search step, CGS assumes that an item is identified as to whether it is a target or a distractor. This identification process is modelled as a drift diffusion process which is also used to describe the behaviour of SAIM-WTA’s nodes. However, instead of simulating the drift diffusion process Moran et al.
( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) used the Wald distribution to represent the distribution of the identification time (i.e., passing of threshold): with the three parameters identification drift rate ( ), identification threshold ( ) and noise level ( ). The noise level was fixed at 0.1 throughout the studies. The total reaction time is the sum of all identification times from all search steps. ( Moran, R., Zehetleitner, M., Mueller, H.
J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) also chose this distribution as Palmer et al. M., Horowitz, T.
S., Torralba, A., & Wolfe, J. What are the shapes of response time distributions in visual search? Journal of Experimental Psychology: Human Perception and Performance, 37, 58– 71., ) found this distribution to be the best to describe Wolfe et al.’s ( Wolfe, J.
M., Palmer, E. M., & Horowitz, T.
Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311.
Doi: 10.1016/j.visres.2009.11.002, ) data. Note that mathematically the probability distribution of the sum of independent random variables can be determined by convolving the probability distributions of the individual random variables. Hence, CGS’s total reaction time can be described as multiple convolutions of a Wald distribution where the number of convolutions depends on the number of search steps.
One consequence of this convolution is that CGS’s RT distribution is more skewed the more search steps take place. Hence, CGS should produce an increase in skewness with increasing display size (depending on the search task). This relationship should enable CGS to model RT distributions from visual search tasks. CGS also assumes that at the response execution stage an erroneous response can occur due to a motor error with a certain probability ( ). Since the identification stage is assumed to be perfect, misses of targets can only occur through motor errors. It is also worth noting that motor errors can “correct” misses as it is possible that search terminates without finding the target but due to an error the model still reports “target present”.
Finally, a residual time accounts for the duration of processes which are outside the actual search process such as encoding of items, post-decisional processes, response planning and execution. The residual time is assumed to be distributed as a shifted exponential distribution with non-decision shift time ( ) and non-decision drift time ( ) as parameters. Discussion Apart from implementing two different types of searches, the models relate differently to the neural substrate.
SAIM-WTA aims to be “biologically-plausible” while CGC is less rooted in neural processes, even though the identification stage has a similar link (drift diffusion model) to neural processes as SAIM-WTA. Both models assume item identification plays a critical role in visual search.
The selection process from the saliency map is seen by CGS’s authors as an approximation of a competition process (hence competitive Guided Search). However, the approximation does not involve interference between items as SAIM-WTA implements. Hence, the selection process is probably better understood as a randomized selection process which is modulated by item saliency.
However, for the purpose of this paper these differences and commonalities are less important. More important is the fact that SAIM-WTA has fewer free parameters than CGS. SAIM-WTA absorbs CGS’s stages (identification stage, encoding stage, etc.) into the competition process. Hence, a numerical comparison between the models can look at whether this more parsimonious model is more successful than a more complex model. Method Both models were fitted to each participant separately. The resulting quality of fit and parameter settings were averaged in order to represent the population level.
The best fitting parameter settings were determined using the maximum likelihood principle (MLP). MLP allows us to base model fit on RT distributions. To employ MLP, traditionally it is necessary for models to possess an analytic probability density function (pdf). However, models such as SAIM-WTA or GCS don’t possess such pdfs. Recent developments in model fitting, often termed approximated Bayesian computation (ABC) or “likelihood-free methods” (see Beaumont, Beaumont, M. Approximate Bayesian computation in evolution and ecology.
Annual Review of Ecology, Evolution, and Systematics, 41, 379– 406. Doi: 10.1146/annurev-ecolsys-121, for a review) solve this issue by approximating the model’s pdfs. We utilized a likelihood-free method based on a KDE-approach which estimates the model’s pdf for a given parameter setting using Monte Carlo sampling (see Turner & Sederberg, Turner, B.
M., & Sederberg, P. A generalized, likelihood-free method for posterior estimation. Psychonomic Bulletin & Review, 21(2), 227– 250. Doi: 10.3758/s13423-013-0530-0, ). In the following section, we will introduce the KDE-method we used here.
After that, we will discuss the method we used to find the best-fitting parameters. Since the representation of RT distributions and the method for parameter search are different from Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) methods, we include a brief explanation of why we have chosen different methods. At the end of this section we will explain how we removed outlier parameter settings. Model’s pdf In this paper, we utilize a novel KDE method, on-line KDE (oKDE; Kristan et al., Kristan, M., Leonardis, A., & Skočaj, D.
Multivariate online kernel density estimation with Gaussian kernels. Pattern Recognition, 44(10), 2630– 2642. Doi: 10.1016/j.patcog.2011.03.019, ). The method was chosen as it is ideal for approximating RT distributions even with 100 trials (see for a demonstration). Originally, the KDE method was proposed by Silverman ( Silverman, B.
Density estimation for statistics and data analysis. London: Chapman and Hall. A KDE is based on a sum of distribution kernels (either Gaussian or Epanechnikov distributions).
The number of kernels is equal to the number of data points. The mean of each kernel is the value of the corresponding data point and the variance for all kernels (bandwidth) is estimated from the data’s variance (see Van Zandt, Van Zandt, T. How to fit a response time distribution. Psychonomic Bulletin and Review, 7, 424– 465. Doi: 10.3758/BF03214357, for details). The oKDE method is more flexible in terms of number of kernels and their variance. In fact, oKDE optimizes the number of kernels and their widths (see ).
Hence, oKDE leads to a more efficient and more adaptable KDE than the standard KDE method (Kristan et al., Kristan, M., Leonardis, A., & Skočaj, D. Multivariate online kernel density estimation with Gaussian kernels. Pattern Recognition, 44(10), 2630– 2642. Doi: 10.1016/j.patcog.2011.03.019, for detailed discussion). Initially, the oKDE method assumes a kernel for each data point (similar to the traditional KDE-approach) and determines the smallest bandwidth for this initial KDE using an optimality criterion.
Subsequently, oKDE clusters these kernels to construct kernels with larger bandwidths (see Kristan et al., Kristan, M., Leonardis, A., & Skočaj, D. Multivariate online kernel density estimation with Gaussian kernels. Pattern Recognition, 44(10), 2630– 2642. Doi: 10.1016/j.patcog.2011.03.019, for details). Parameter search To find the optimal parameters, we utilized a particular version of a differential evolution (DE) algorithm (Storn & Price, Storn, R., & Price, K. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces.
Journal of Global Optimization, 11(4), 341– 359. Doi: 10.1023/A:328,; ter Braak, ter Braak, C. A Markov chain Monte Carlo version of the genetic algorithm Differential Evolution: Easy Bayesian computing for real parameter spaces. Statistics and Computing, 16, 239– 249.
Doi: 10.1007/s11222-006-8769-1, ). DE algorithms aim to implement a near global search through parameter space by utilizing populations of parameter settings (rather than a single parameter setting) as the starting point for the search (see Comparison with Moran et al.’s Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24method for more details). The particular version we used was the probabilistic Markov chain Monte Carlo (DE-MCMC) extension by Turner, Sederberg, Brown, and Steyvers ( Turner, B.
M., Sederberg, P. B., Brown, S. D., & Steyvers, M. A method for efficiently sampling from distributions with correlated dimensions. Psychological Methods, 18, 368– 384.
Doi: 10.1037/a0032222, ). A main advantage of the differential algorithms is their natural ability to deal with correlations between parameters.
For instance, accumulation rate and decision boundary are correlated as an increase in decision boundary leads to an increase in reaction times in a similar way as a decrease in accumulation rate leads to an increase in reaction times. Likelihood function The fit of the model with the data was evaluated with the likelihood principle using a pdf for mixed data (Turner & Sederberg, Turner, B. M., & Sederberg, P. A generalized, likelihood-free method for posterior estimation. Psychonomic Bulletin & Review, 21(2), 227– 250.
Doi: 10.3758/s13423-013-0530-0, ): where P( s 1) is the probability of correct response and P( s 2) is the probability of incorrect response. M j( x i θ) denotes the model’s pdf for any observation x i, the parameters θ and response type ( j).
As stated earlier, here the model’s pdf is represented by a KDE. However, this likelihood function is not fully suitable for our modelling approach, as we don’t consider the reaction times for incorrect responses. Therefore, Turner and Sederberg’s ( Turner, B. M., & Sederberg, P. A generalized, likelihood-free method for posterior estimation.
Psychonomic Bulletin & Review, 21(2), 227– 250. Doi: 10.3758/s13423-013-0530-0, ) equation turns into: where n i indicates the number of incorrect responses and n c is the number of correct responses. P( X c) is the probability of correct responses in the model. In addition, we improved the robustness of estimating the likelihood function at unlikely data points by introducing a dataset-defined threshold for the model’s pdf.
Note that thresholding very small pdf values is common practice to avoid numerical issues (i.e., underflow) in the calculation of likelihood values. In standard applications, this practice does not lead to large problems as the model’s pdf is typically similar to the data (e.g., Weibull distribution as model of RT distributions) and so small pdf values relate to rare occurrence of data points. However, in our modelling enterprise the model’s pdf needs to be created via Monte Carlo sampling which sometimes leads to a misrepresentation of the model’s pdf particularly for unlikely simulation outcomes (i.e., unlikely data points). In other words, the KDE constructed from such a sampling error assigns small probabilities to these data points; even smaller than implied by their presence in the dataset. Other sampling runs with similar parameter settings may assign reasonable probabilities to these data points.
Such variations in sampling can lead to large problems in finding optimal parameters during the parameter search. To stabilize this (i.e., improving the robustness of estimating the likelihood function), we introduced this data-defined threshold. In order to determine this threshold, we fitted a KDE to the dataset. As stated earlier, initially the oKDE method assumes a kernel for each data point (similar to the traditional KDE approach) and determines the smallest bandwidth for this initial KDE using optimality criteria. This bandwidth defines a lower bound for a probability of a data point.
Hence, any pdf constructed for a model (KDE) should produce at least this probability for each data point. Therefore, this bandwidth forms a reasonable threshold for the model’s pdf (KDE). In other words, if the model is correct, a failure to produce reasonable probabilities for unlikely data points has to be due to the sampling error and thresholding the model’s KDE in this situation corrects this error. However, sampling error is not the only reason for failing to produce reasonable probabilities. Suboptimal parameter settings can lead to model pdfs which are very different from the data’s pdf. In this situation, the threshold introduces a bias towards a better evaluation of the model. To lower this bias, we reduced the data-driven threshold by 50%: where h is the smallest bandwidth.
Comparison with Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) methods To fit parameters, Moran et al. ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) used the popular algorithm by Nelder and Mead ( Nelder, J. A., & Mead, R. A simplex method for function minimization. The Computer Journal, 7, 308– 313. Doi: 10.1093/comjnl/7.4.308., ) which is implemented in MatLab’s fminsearch.
This method is very sensitive to the choice of the starting point of the parameter search. Our DE-MCMC method reduces this problem by using a population of starting points. This sensitivity to the starting point of a search is because complex models like the ones used here have many local solutions. These local solutions are the best solutions in particular areas of the parameter space, but it is not clear whether a particular local solution is the overall best solution (global solution). Most, if not all, methods for parameter search find (get trapped in) local solutions and cannot guarantee that this is the global solution.
Amongst other factors the starting point of the search is critical for which local solution is found. Broadly speaking, search algorithms tend to find local solutions near the starting point. Moreover, to estimate the RT distributions Moran et al. ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) employed the commonly used Quantile Maximal Probability (QMP) method by Heathcote, Brown, and Mewhort ( Heathcote, A., Brown, S. D., & Mewhort, D. Quantile maximum likelihood estimation of response time distributions.
Enterprise Architect 10 Full Serial Guller 1
Psychonomic Bulletin and Review, 9, 394– 401. Doi: 10.3758/BF03196299, ). However, Turner and Sederberg ( Turner, B.
M., & Sederberg, P. A generalized, likelihood-free method for posterior estimation. Psychonomic Bulletin & Review, 21(2), 227– 250. Doi: 10.3758/s13423-013-0530-0, ) showed that this method can lead to misleading results. Thus, given the differences between our approach and Moran et al. ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ), attempting to replicate Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) parameter settings is unlikely to be successful. However, to demonstrate that our approach is more reliable than Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) approach, we fitted CGS to Wolfe et al.’s (2013) data twice, using different starting points. First, Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H.
J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) parameter settings from the individual participants were used as starting points for the parameter search. Even though these starting points are unlikely to be the best fits given the differences in methods, they should at least be close to very good solutions which DE-MCMC would be able to find. Second, we used our parameter settings established by fitting Lin et al.’s (2015) data.
Interestingly, the quality of fit for Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions.
Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) parameter settings as starting points was not as good as for our parameter settings as starting points. Hence, we conclude that our parameter settings generalize better across different datasets while Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) settings seem very specific to their chosen starting point of the search. Removal of outlier parameter settings It turned out that some participants’ parameter settings were extreme. We therefore applied an outlier elimination method, the median absolute deviation (MAD; Leys, Ley, Klein, Bernard, & Licata, Leys, C., Ley, C., Klein, O., Bernard, P., & Licata, L. Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median.
Journal of Experimental Social Psychology, 49(4), 764– 766. Doi: 10.1016/j.jesp.2013.03.013, ), to each parameter in each task. As criterion for an outlier we used five standard deviations. A participant was identified as outlier if at least one parameter value was considered to be an outlier. This participant was removed from the further analysis. Results and discussion: SAIM-WTA We fitted SAIM-WTA with three free parameters (distractor saliency, decision boundary, accumulation rate) to Lin et al.’s ( Lin, Y-S., Heinke, D., & Humphreys, G. Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework.
Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ) 58 datasets from three visual search experiments (feature search, conjunction search, spatial configuration search). Hence, we obtained 58 parameter settings (see for values), 19 parameter settings (participants) for feature search, 19 settings (participants) for conjunction search and 20 settings (parameters) for spatial configuration. Eyeballing the parameter settings, we noticed that there were a few settings which could be considered as outliers. Our outlier detection procedure led to the removal of two participants from feature search, three settings from conjunction search and no participant from spatial configuration search. To assess the overall fit for each participant we calculated the log likelihood ratios (log likelihood value from the model divided by the log likelihood value of the KDE’s dataset; see for the results). We compared ratios from the different tasks with the Wilcoxon rank-sum test and found a significant decline of ratios between feature search and conjunction search ( ); and feature search and spatial configuration ( ).
There was no significant difference between conjunction search and spatial configuration search ( ). To illustrate the quality of fit (likelihood ratio), shows the outcome from three participants.
Note that the choice of these participants was made randomly by MatLab to avoid an author bias. The likelihood ratio was −46.32 for feature search, −61.10 for conjunction search and −71.98 for spatial configuration search. The graphs indicate that SAIM-WTA was able to produce an increased skewness with increased display size. This increase broadly matched the increase of skewness in the data, but not to the same degree. The failure to match skewness is particularly pertinent in spatial configuration search for display size 18.
This effect is illustrated in where the likelihood ratio declined with increasing display size. Nevertheless, it is important to note that the only source of this effect is the increase of number of distractors in the input of the model since all parameters are kept constant. In other words, the competition between items due to lateral inhibition is able to explain the skewness found in the visual search. Shows how the three free parameters (distractor saliency, decision boundary, accumulation rate) changed across the three tasks. The parameters were entered into a Wilcoxon rank-sum test. For accumulation rate, there was significant difference between feature search and conjunction search ( z = 4.845, p. Results and discussion: Competitive Guided Search We fitted CGS with seven free parameters (target saliency, identification drift, identification threshold, quit weight increment, non-decision time shift, non-decision time drift, motor error) to Lin et al.’s ( Lin, Y-S., Heinke, D., & Humphreys, G.
Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework. Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ) 58 datasets from three visual search experiments, feature search, conjunction search and spatial configuration search. Thus we obtained 58 parameter settings (see for values), 19 parameter settings (participants) for feature search, 19 settings (participants) for conjunction search and 20 settings (parameters) for spatial configuration. Our outlier removal procedure detected no outlier for feature search, two outliers for conjunction search and two outliers for spatial configuration. It is also worth noting that the parameter search revealed that there are good fits for conjunction search and feature search where the saliency values are implausibly high.
This is not very surprising as fast target searches can be executed with arbitrarily high saliency value. To solve this problem, we first fitted spatial configuration and used these resulting parameter values as starting point for fitting the other searches. This way the best fits produced saliency values which were relatively small (see note 1). To assess the overall fit for each participant, we calculated the log likelihood ratios, i.e., log likelihood value from the model divided by the log likelihood value of the KDE’s dataset. We compared ratios from the different tasks with the Wilcoxon rank-sum test and a significant difference was found between feature search and conjunction search ( ); and feature search and spatial configuration search ( ).
And there was no significant relation between conjunction search and spatial configuration search ( ). Shows that the quality of fit declined with task difficulty. To illustrate the quality of fit, shows the outcome from three participants.
Note that the choice of these participants was made randomly by MatLab to avoid an author bias. The likelihood ratio was –18.44 for feature search; −38.82 for conjunction search and −44.10 for spatial configuration search.
The graphs illustrate that CGS’s distributions nicely overlap with the RT distributions from the respective tasks. Hence, we were able to qualitatively replicate Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) results.
Results of fitting CGS. The top-left graph shows the mean log-likelihood ratios (quality of fit) for the different tasks. The remaining graphs show the means of CGS’s seven parameters for the three tasks (Feature Search = FS; Conjunction Search = CS; Spatial configuration search = SC). Note, for the purpose of a better illustration the target saliency parameter was scaled logarithmically. The results replicate Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H.
J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) findings. The error bars indicate the standard error. Results of fitting CGS. The top-left graph shows the mean log-likelihood ratios (quality of fit) for the different tasks.
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The remaining graphs show the means of CGS’s seven parameters for the three tasks (Feature Search = FS; Conjunction Search = CS; Spatial configuration search = SC). Note, for the purpose of a better illustration the target saliency parameter was scaled logarithmically. The results replicate Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions.
Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) findings. The error bars indicate the standard error.
Interestingly, we were also able to replicate the qualitative relationship of parameter values with the search tasks (see and Moran et al. ( Moran, R., Zehetleitner, M., Mueller, H.
J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ); Appendix C). The parameters accounting for encoding and post-decisional process showed longer delay (non-decision shift) and more variance (non-decision drift) with increasing task difficulty. Motor error increased with task difficulty. The identification drift showed slower accumulation rate with increasing task difficulty.
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The identification threshold decreased with task difficulty (albeit counterintuitively). The likelihood to stop scanning the search display (w quit) increased less the more difficult the task was. Finally, the guidance (target saliency) was smaller the harder the task was. Interestingly, and similar to Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) findings, there was still residual guidance in the spatial configuration search task. In fact, there was no significant difference between our guidance parameters and Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions.
Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) parameters (see for a comparison using Wilcoxon rank-sum test). These findings question Moran et al.’s ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M. Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24.
Doi: 10.1167/13.8.24, ) explanation for their result. They stipulated that guidance may be possible due to the fact that participants were highly practiced in Wolfe et al.’s ( Wolfe, J. M., Palmer, E.
M., & Horowitz, T. Reaction time distributions constrain models of visual search. Vision Research, 50(14), 1304– 1311. Doi: 10.1016/j.visres.2009.11.002, ) dataset. However, in Lin et al.'
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S ( Lin, Y-S., Heinke, D., & Humphreys, G. Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework. Attention, Perception, & Psychophysics, 77(3), 985– 1010. Doi: 10.3758/s13414-014-0825-x, ) experiment the participants were not practiced and CGS still suggests that there is guidance involved. Since our numerical methods were different from Moran et al.' S ( Moran, R., Zehetleitner, M., Mueller, H. J., & Usher, M.
Competitive guided search: Meeting the challenge of benchmark RT distributions. Journal of Vision, 13(8), 24– 24. Doi: 10.1167/13.8.24, ) methods, as discussed earlier, we also fitted CGS to Wolfe et al.’s ( Wolfe, J. M., Palmer, E.
Visual flexibilityCustom drawing styles let you choose how to represent design elements with custom shapes, transparencies, colors and images. Unleash your creativity and build the visual representations your customers are familiar with.Let your imagination run wild - custom drawing stylesStreamline your diagram's appearance with the new 'Simple' diagram style. As a drawing style, it is minimalist, removing notation-specific detail, leaving uncluttered diagrams that are easily understood by all stakeholders. Any detailed design diagram, using the correct element types, can be easily rendered in this simple format, ensuring a change to the detailed model is updated in the view presented to the non-technical staff.For Executives, Architects and Business UsersThis drawing style is frequently used by architects, business users, executives and many others as a preferred means of conveying custom information concerning a business capability, architecture, system interaction and many other scenarios.
Coupled with WebEA and Prolaborate, this offers end users instant access to attractive and familiar diagrams that avoid the general 'dullness' of UML and other technical diagrams. GovernanceTake advantage of model based add-ins to enforce new work flows, governance and control within your mission critical models.
Leverage the security group based restrictions on Perspectives (technologies) and Ribbon sets to ensure your modelers see only the tools and technologies relevant to them.Add-ins that are defined in the modelModel Based Add-Ins are designed to ease development and deployment of custom add-ins. It provides a platform for add-ins that are defined within the model itself and therefore do not require network staff or others to manage the update and deployment cycleSignificant features and capabilities include:. Add-ins are defined in the model using standard modeling techniques. JavaScript supported for all behavioral code. Add-ins can:. Access all Repository based behavior. Respond to repository events (signals).
Set up and use property lists. Call SBPI based API's. Activated Add-InsActivating a dynamic add-in is a security controlled process in which an admin or authorized person may select from the list of add-ins defined within a model and check those which are active and deselect those that are not authorized or ready to run. Activated add-ins will run when the model is opened and be torn down when the model closes.Publish Add-InsDynamic add-ins can be published as XMI and re-used in different models, giving the flexibility to:. Publish a range of dynamic add-ins using the Reusable Asset Service (RAS). Develop a version of an add-in in a test repository and when ready, import it into the production model using XMI. Custom TablesCustom Tables provide a flexible option to define your own tabulated information in an Element viewable on a diagram.
Typical uses may include SWOT analysis or a capability matrix where table based information needs to be included in the model.Custom tables support:. User definition and population of the tables. Typical table formatting including setting cell colors and borders, alignment, adding cells as well as merging cells. Automation feature to compute row values based on model data. Ability to fill from SQL query on a package (mini matrix) when using automation. Model Based Add-InsModel Based Add-Ins are designed to ease development and deployment of custom add-ins. Security AwarePerspective sets associated with security groups on a per model basis allow administrators and business owners to customize the view and scope of particular modeling staff based on their area of concern and capability.
For example, business modelers used to working with BPMN could be limited to working with the BPMN technology, removing all unnecessary perspective and technology sets from their interface when they are in a particular model. Likewise, particular menu ribbons can be hidden to further customize and focus the modelers workspaceNew Perspective GroupsVersion 15 improves on the Perspectives sets offered in previous editions by supporting additional perspective sets and including more generic sets that incorporate a wider range of material in a single set.
For example, there is now an 'All Business Modeling' perspective that aggregates all perspectives under the business modeling folder. New Element BrowserThe Element Browser has been moved from a separate docked window to form part of the Browser suite. This allows users to quickly find and use this window to drive other aspects of their model such as Features, Tasks, Responsibilities, Discussions, Reviews etc.The Element Browser also has an improved context menu to drive advanced editing capabilities from the Element Browser. For example, access the Structured Scenario editor for a Scenario easily and quickly from the Element Browser context menu on a Scenario, or connect with an integration element directly from tools like Jira and ServiceNow. Diagram BrowserThe Diagram Browser is a new tab in the Browser named 'Diagram'.
This provides a view of elements within the currently viewed diagram. Primary use will be to allow rapid selection and navigation of a diagram based on the elements only shown in that diagram. Click an element in Browser to highlight in diagram. Select element in Browser when clicked in diagram.
Search the Browser for a particular elementThe Diagram Browser is a great addition to Enterprise Architect and supports modelers who are tightly focused on their visual representation and value a filtered set of elements in the browser tree that are only those located on the current diagram. Finding elements in a large diagram is now simplified using the filtering capability of the Diagram Browser - in conjunction with its ability to highlight and center an element when selected in the Tree. Business Motivation Model (BMM)The BMM model provides a blueprint designed to support a range of methodologies. Decision ServiceAllows users to create Decision Service elements and specify output/encapsulated decisions and input data as the interface. By providing data sets for the inputs, Enterprise Architect is able to simulate the decision graph involved in the Decision Service. A Decision Service could serve as a reusable element, which might be invoked internally by another decision in the Decision model, or externally by a task in a BPMN process model.DMN Bindings to Model ElementsAllows users to create a DMN instance specification that binds element properties to input fields of a DMN model.
This allows such things as tagged values with a dollar cost or weight or other data property of interest to be consumed and piped into the decision graph. This results in strong support for customized decision modeling about any topic.DMN Bindings to Model ElementsAllows users to create a DMN instance specification that binds element properties to input fields of a DMN model. This allows such things as tagged values with a dollar cost or weight or other data property of interest to be consumed and piped into the decision graph. This results in strong support for customized decision modeling about any topic. New Icon Rendering EngineDisplay of icons at high DPI settings are now vastly improvedTo facilitate a better and cleaner appearance, all the major icons in the Browser are now hand rendered at the right scale for the current DPI setting, resulting in a cleaner and more exact image.In addition, the icons have been reworked into colors matching the color sets for diagrams, greatly improving modeling consistency and UI appeal. For example, Packages, Classes, Use Cases and other UML elements have been re-colored to match the version 15 color sets applied from the default version 15 diagram theme. These icons also appear in package elements in diagrams where the visibility options have been configured to show Package Contents.Icons rendered to the diagrams are now rendered natively to the current zoom level and DPI scaling.
This is present for any tree structure (like the project browser) as well as on diagrams in package lists and the like. Other Changes. MariaDB ODBC driver now supported.
Document generation now provides new report constant: ReportFilenameShort. Package Browser and Gantt View context menu option added for opening the selected Package as a list or Gantt view. DB Explorer window now supports reload using tab context menu. XMI export performance improved for models with test points defined. Saving of cached images and documents for WebEA improved.
New project option added to set the minimum build number required to access a project. Changes:Everything you need to manage change elements inside Enterprise Architect. Show the Changes windows, quickly see verified changes, new changes and incomplete changes.
Searches and charts for recently requested changes and recently completed changes also available.Defects:Show the defects window, search for verified defects, new defects and unresolved defects. Search and chart recently reported defects and recently resolved defects.Issues:Show the issues window, search for verified issues, new issues and unresolved issues. Search and chart new issues and unresolved issues.Tasks:Show the tasks window, search for verified tasks, new tasks and incomplete tasks. Search and chart new tasks and incomplete tasks.Events:Show the events window, searches for high priority and open events. Search and chart recently reported events and recently completed events.Decisions:Show the decisions window, search on verified decisions, new decisions and decisions with no effective date. Search and chart on recently created decisions, and recently effective decisions. The Document view allows you to open and edit Linked Documents in line with the diagram view.
Rapidly switch between linked documents by single clicking elements in the project browser, diagrams or search results.The Document view also gives you access, through a handy draw down menu, to edit and reload the document, as well as setting the default zoom. Two new searches have been added giving quick access to all elements in the model with linked documents - or just the ones that have been modified recently. Enterprise Architect 13 allows you to easily compare 'As-Is' and 'To-Be' models, being able to analyze a diagram to see exactly what changes occur at every iteration. Simply select the package or diagram you would like to change and use the Context Menu to 'Clone Structure as New Version'Now you can make changes to subsequent versions without altering the underlying structure of the 'As-Is' diagram. This Cloning approach provides substantial benefits and allows you to take a snapshot in time of model development. OpenModelica can interpret complex mathematical results from your SysML model by producing compelling graphs that contain rich detail.
The example image graphs a bouncing ball modeled in a SysML model and produces an OpenModelica plot of the height over time.This graph can then be used to interpret a range of factors from gravity, height, object mass and other integral system components that may not be apparent from the underlying SysML model. Bring the power of mathematical analysis into the heart of Enterprise Architect. Watch introductory video webinar recordings, read the step-by-step instructional guides, easily search the online Enterprise Architect User Guide.
Reviews, Articles and More:. Enterprise Architect Reviewers Guide:. Product Overview:. Enterprise Architect Editions:. Webinar Recordings:. Tutorials:. Demo Videos:.
White Papers:Latest Help Topics in PDF format:. Fundamentals:. Modeling Domains:. Publishing:.
Time Aware Modeling:. Parametric Simulation using OpenModelica:. The Schema Composer:. Reuseable Asset Service (RAS).
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