Analyzing Spatial Models of Choice and Judgment with R

Consumer Behavior in the Choice of Mode of Transport: A Case Study in the Toledo-Madrid Corridor
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This package includes pricing function for selected American call options with underlying assets that generate payouts. Animal track reconstruction for high frequency 2-dimensional 2D or 3-dimensional 3D movement data. A collection of functions for estimating centrographic statistics and computational geometries for spatial point patterns. Bayesian bandwidth estimation and semi-metric selection for the functional kernel regression with unknown error density.

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Deconvolution density estimation with adaptive methods for a variable prone to measurement error. An application programming interface for generating null models of social contacts based on individuals' space use. Data-Informed Link Strength. Combine multiple-relationship networks into a single weighted network. Impute fill-in missing network links. The experimental setup is specified in the main window Figure 1a. Pathfinder can automatically calculate the position and size of the maze and the goal location provided they are constant across trials , or these parameters can be entered manually.

The chaining corridor is centered on the goal platform and extends throughout all 4 quadrants; its width is specified in the main window. The larger thigmotaxis zone is specified in the main window; Pathfinder calculates the smaller thigmotaxis zone as half the width. Heading error is the angular distance between the actual path direction and a straight line to the goal Pathfinder calculates average heading error at all points; only a single example shown. The width of the corridor in degrees is specified in the main window and is centered on the goal.

The distance from the platform is measured at each timepoint provided by the tracking software actual path; only a fraction of distances shown for clarity to provide a cumulative distance measure. Assuming the same swim speed as the actual path, distances are similarly summed from the ideal path, to provide a cumulative ideal path measure.

Ideal Point Models as a Subset of Statistical Measurement

The ideal cumulative distance is subtracted from the actual cumulative distance to generate the IPE. Pathfinder relies on several variables that describe navigation relative to the pool and platform geometry: 1 Ideal Path Error IPE : the summed error of the search path Figure 1c. It is conceptually similar to the Cumulative Search Error CSE since it also measures proximity to the goal throughout the trial 9 , When calculating the IPE, the distance from the goal is measured at each time point in the trial and summed to generate a cumulative distance measure of the actual path similar to CSE.

In contrast to the CSE, the IPE is calculated by subtracting the cumulative ideal path distance from the cumulative actual path distance.

idealstan: an R Package for Ideal Point Modeling with Stan

The cumulative ideal path is simply the sum of all of the distances between the goal and the position of the animal if it swam along a straight line to escape, using the average velocity from the trial. The current path direction is defined by a line connecting two temporally-adjacent xy coordinates.

The average heading error is an average of all of the heading error values for the trial and the initial heading error is the average of the heading error values for the first second of the trial. Additional variables are user-defined on the main window: 3 Angular Corridor Width: the size of the angular navigational corridor in degrees that extends from the start location and widens towards the goal, centered on the goal location.

This can be used to measure performance and characterize strategies with respect to multiple goal locations e. This is necessary, for example, to measure direct trajectories to a former goal location in a reversal paradigm since the strategy will no longer meet direct path criteria if the former location in contacted and search continues elsewhere in the maze. Once the variables are defined, boundaries must be set to establish the criteria for strategy categorization. These categories are mutually exclusive and follow a defined order 1 to 8 , but the user can opt to exclude strategies from the analysis.

Thus, Pathfinder determines, in a stepwise fashion, whether a given trial fulfills the criteria for direct swim. If so, it moves on to categorize the next trial. If not, it determines whether the trial fits the subsequent strategy, and so on.

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Social psychology Tenth ed. Richard E. Pathfinder can also open files exported from the open source tracking software, ezTrack 26 , enabling a cost-effective and fully open source workflow for detailed water maze behavioral analyses. E-mail deze pagina. Abstract Within the context of the consumption of goods or services the decisions made by individuals involve the choice between a set of discrete alternatives, such as the choice of mode of transport. American Journal of Political Science, 57 4 :

The strategies and their parameters are shown in Figure 2. In the output file. Pathfinder also has the ability to calculate the entropy for each trial, a measure of disorder in the path, relative to the goal location. Entropy measures the performance by looking at a shift from more disordered swimming high entropy to more spatially strategic paths low entropy , and has been previously found to be highly sensitive to water maze search performance Due to the manipulation of large matrices, calculating the entropy of trials is very slow.

Pathfinder categorizes each trial according to 1 of 8 possible strategies. Categorization proceeds sequentially in the order shown unless some strategies are excluded from the analysis. For example, for a trial to be classified as Random Search, the path must cover a minimum proportion of the maze and not fit any of the criteria for strategies 1—6. In the examples shown, the blue square indicates the start point and the green circle indicates the middle of the pool. Parameter settings are those used in the present study and should be adjusted depending on changes to testing procedures and maze geometry.

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Occasionally, some trials cannot be categorized. The user therefore has the option to manually categorize uncategorized trials, by selecting this option on the main window. Additionally, there is an option to manually categorize all trials. Here, Pathfinder provides an image of the trial as well as shortcut keys to select the appropriate strategy.

The software will also display the strategy it had automatically categorized for the displayed trial. Manual categorization will not overwrite the automatic categorization but will be displayed separately in the output file. This allows for comparison between the automatically calculated and user-selected strategy. In addition to strategy categorization, Pathfinder will also create heatmaps as a useful visual representation of groups of trials.

This is accomplished by counting the number of times animal s visit each bin in a hexagonal array that is overlaid on the maze bin size is user-defined. The range of colors cool to warm can be automatically set to occupy the full scale. Alternatively, the user can manually set the maximum, above which all bins will read the hottest.

Maximum Likelihood Estimation of Spatial Models: Principles

Mice were housed under a reversed light-dark cycle lights off am—pm and completed water-maze testing in the dark phase. Mice were first tested on the Barnes maze 29 and were 18 weeks old when tested on the water maze for the current experiment. All efforts were made to minimize animal suffering, and all procedures adhered to guidelines from the Canadian Council on Animal Care and were approved by the Dalhousie University Committee on Laboratory Animals.

Spatial water maze training. The water maze consisted of a plastic circular pool cm diameter painted black. A circular escape platform 14 cm height, 9 cm diameter was positioned 1 cm below the water. The water maze was placed in a diffusely lit room with many extra-maze visual cues posters on walls, a desk, the experimenter, geometric layout of testing room etc. Animals were tested over a total of 15 days. Across trials, mice were released into the pool from four different locations, with the order differing across mice. They were given a maximum of 60 sec to locate the escape platform, after which they were guided to the platform by the experimenter.

Mice remained on the platform for 15—20 seconds before being removed from the pool. During daily test sessions, mice were tested in squads of 4 and each mouse was held in separate cages filled with a bedding of paper towel. The inter-trial interval ranged from 2—8 minutes.

The day following acquisition training, memory was assessed with a single sec probe trial with no escape platform present. Mice then completed a single day of re-training Retrain to reduce extinction that may occur during the probe trial. During re-training the escape platform is returned to the same location used in acquisition training.

After acquisition re-training, reversal learning was assessed over 3 days R1-R3 with the escape platform moved to the opposite side of the maze.

A reversal probe trial R probe was then completed to assess memory for the location of the new escape platform location. Finally, a single day of visible platform training Visible platform; 4 trials was completed, where the escape platform was moved to a new location and made visible with the addition of a striped flag. Behavior was recorded with the WaterMaze Actimetrics video tracking system 5 samples per second , via a camera placed directly above the pool. To validate Pathfinder, we trained mice for 8 days on a spatial water maze such that they achieved asymptotic performance according to standard metrics and should therefore have adopted distinct navigational strategies as they learned the procedural and spatial task demands.

Following acquisition, mice received an unreinforced probe trial, 1 day of retraining, 3 days of reversal training platform in opposite side of pool , another probe trial, and one day of visible platform training outlined in Figure 3a. Individual performance metrics were analyzed for acquisition b — f and reversal g — k stages of testing. Asterisks denote statistically significant differences from the subsequent days that are indicated by the numbers. To confirm that mice learned the task, we first analyzed performance using several metrics that indicate learning but do not reveal details about navigational strategies Figure 3.

We focused on acquisition and reversal phases since they are the main focus of our subsequent strategy analyses. Over the 8 days of acquisition, mice reached the platform faster, increasingly swam in the direction of the platform as measured by heading angle error and had lower IPE and entropy scores.

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The greatest performance improvements occurred during the first 4 days and, while all measures revealed improvements beyond day 4, only average heading error and entropy analyses revealed improvements beyond day 5. There were no sex differences in acquisition performance. Reversal learning performance improvements were mostly apparent after the first day of training, likely because mice had learned the procedural aspects of the task and the spatial environment, and only had to learn a new platform location Figure 3g—k Path entropy decreased from days 2—3, indicating continued learning.

Females and males were equivalent in all performance measures except males had a lower initial heading error on day 1 of reversal training Figure 3h. Pathfinder revealed clear differences in search strategies over days of training Figure 4.

Analyzing Spatial Models of Choice and Judgment with R

Over the first two days of acquisition, mice were initially thigmotaxic. After learning that the pool wall did not afford escape, they then transitioned to chaining, random and scanning search patterns, all of which indicate spatially non-specific search away from the pool wall. A similar proportion of trials were indirect searches over days 2—8 of training.

There were no major sex differences in strategy. The usefulness of strategy analyses at least with default settings for long probe trials is limited since spatially-specific strategies rely on IPE, which rapidly increases with trial duration. Additionally, animals will change strategies as they learn that the escape platform is not available in the expected location.

Indeed, when the probe trial analysis was restricted to the first 10s, mice displayed focal and directed search strategies, indicating perseveration at the former platform location.