© 2013 American Psychological Association 0278-7393/14/$12.00 DOI: 10.I037/a0035279
Joumal of Experimental Psychology: Leaming, Memory, and Cognition 2014, Vol. 40. No. 2, 602-608
RESEARCH REPORT
Differentiating Spatial Memory From Spatial Transformations Whitney N. Street and Ranxiao Frances Wang University of IlUnois at Urbana-Champaign The perspective-taking task is one of the most common paradigms used to study the nature of spatial memory, and better performance for certain orientations is generally interpreted as evidence of spatial representations using these reference directions. However, performance advantages can also result from the relative ease in certain transformations/rotations. To differentiate spatial memory from spatial transformations, the present study took a new approach based on the hypothesis that responses may be biased toward the original representation but not a transformed one. Participants memorized a regular target array and then judged the relative direction between 2 targets while imagining facing various directions. Their response time and absolute errors showed the standard advantages at 4 imagined orientations. In contrast, an attraction analysis suggested that only 1 orientation was represented in memory, whereas performance advantages at other orthogonal orientations were due to lower transformation costs and should not be interpreted as spatial representations. These findings challenged the traditional performance-based interpretations of perspective change tasks and provided a new research paradigm to differentiate spatial representations from spatial transformations. Keyword^: spatial representation, reference frame, perspective taking, spatial transformation
require less response time and lead to higher accuracy (Mou & McNamara, 2002; Rieser, 1989; Shelton & McNamara, 2001; Simons & Wang, 1998; Waller, 2006; Waller, Montello, Richardson, & Hegariy, 2002; Wang, 2007). As intuitive as this paradigm is, it has a major theoretical limitation. Performance in a perspective change task can refiect the nature of the spatial memory, the efficiency of the spatial transformation/spatial reasoning processes, or both. This limitation is particularly prominent when performance advantages are shown for multiple orientations (e.g., Kelly & Avraamides, 2011; Liu, Mou, & McNamara, 2011; Mou & McNamara, 2002). For example. Mou and McNamara (2002) asked participants to memorize a set of objects and make judgments of relative directions (JRD) among them (e.g., imagine you are at X, facing Y, point to Z). They showed that performance was better when the imagined heading was either parallel with or orthogonal to the axis of the layout (the "alignment effect"), thus showing a "saw-tooth" pattern in response time (RT)/accuracy as a function of the imagined heading. According to the traditional performance-advantage hypothesis, these data provide evidence that four reference directions were used in encoding spatial relations among the objects, and misaligned perspectives were transformed from these representations. However, there are at least two alternative hypotheses. First, spatial information might be coded relative to a reference axis (including both directions, e.g., 0° and 180°), whereas performance advantages for directions orihogonal to that axis (e.g., 90° and 270°) was due to minimal cost in making orthogonal transformations. Second, it is also possible that only a single reference direction was used to encode spatial information (e.g., 0° only), and imagined heading along all other directions were inferred from this
Spatial memory is an important cognitive function that is shared by most animal species. Extensive research has been devoted to studying the nature of spatial representations in insects, birds, and mammals, including humans, using various research paradigms such as the novel shortcut tests (e.g., Bennett, 1996; Foo, Warren, Duchon, & Tarr, 2005; Tolman, 1948), landmark/cue manipulations (e.g.. Burgess, 2006; Burgess, Spiers, & Paleologou, 2004; CoUett & Cartwright, 1983; Collett & Rees, 1997; O'Keefe & Speakman, 1987), disorientations (Hermer & Spelke, 1996; Learmonth, Newcombe, & Huttenlocher, 2001; Wang, 2012; Wang & Spelke, 2000, 2002), and so on. Among these paradigms, the perspective change task is one of the most widely used methods in studying human spatial representations. In a typical task, participants leam a set of targets in an environment. They are then asked to make judgments of spatial relations from various perspectives. Performance is taken as an indicator of the underlying representations based on the hypothesis that encoded perspectives are directly retrieved; therefore, they
This article was published Online First December 23, 2013. Whitney N. Street and Ranxiao Frances Wang, Department of Psychology, University of Illinois at Urbana-Champaign. Some of the findings were presented at the 53rd annual meeting of the Psychonomic Society, November 15-18, 2012, Minneapolis, Minnesota. Thanks to Aaron Nachsin, Maria Scheet, Lisa Hutcheson, Anthony Lupo, Shea Kaelin, Juliya Kulbachenko, and Jeremiah Pickert for help with data collection. Correspondence concerning this article should be addressed to Ranxiao Frances Wang, Room 533, Department of Psychology, University of Illinois at Urbana-Champaign, 603 East Daniel Street, Champaign, IL 61820. E-mail: franceswiâ'cyrus.psych.illinois.edu 602
SPATIAL MEMORY AND SPATIAL TRANSFORMATIONS
original representation by spatial transformations. Good performance for the encoded orientation was a result of direct access, whereas good performance for the other three orthogonal orientations refiected efficient spatial transformations for these special angles. The potential confound between spatial representations and spatial transformations exists even when there is only a single preferred orientation (e.g., Rieser, 1989; Shelton & McNamara, 2001; Waller, 2006; Wang, 2007). For example, Shelton and McNamara (2001) showed that when participants leamed an array from multiple directions, performance was best at the leaming direction aligned with the room geometry. These results were usually interpreted as a single orientation-specific representation encoded along the preferred direction. However, it is also possible that the spatial representation itself was orientation-invariant, whereas the performance advantage was caused by the relative ease in reconstructing a mental image of the array from certain orientations due to factors such as symmetry and colinearity. It is vital to distinguish between spatial representations and spatial transformations. However, existing research paradigms based on performance analysis cannot differentiate effects caused by spatial encoding from those caused by the spatial reasoning processes. To address this issue, we took a new approach based on a competition model inspired by previous research on systematic biases in spatial memory (e.g., Huttenlocher, Hedges, & Duncan, 1991; Sampaio & Wang, 2009) and the interference theory of the angular disparity effect (Brockmole & Wang, 2003; May, 2004; Presson, 1982; Wang, 2004, 2005). The competition model assumes that spatial information is encoded in an original represen-
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tation(s). When a task can be solved by directly retrieving information from the original representations (e.g., imagining a perspective coinciding with the encoded one), the original representation is retrieved for the responses. When a task requires spatial information that is not contained in the original representation, spatial transformation is performed to generate a new representation (e.g., imagining what a scene is like from a novel perspective), which is then used to perform the task. However, because there is a discrepancy between the information in the original representation and that in the transformed representation, the original representation may compete with the transformed representation, causing the responses to be biased toward the original representation. On the contrary, the transformed representations are transient and generated only for the current response. Therefore, they should not affect other transformed representations. Finally, when there are multiple encoded representations, the responses should be biased toward the nearest encoded representation. According to this competition model, encoded and transformed representations may be differentiated by examining the attraction effects in the biases. Figure la illustrates the logic of the attraction effect of an encoded representation on the transformed representations. The top portion shows an example of one target at -50° from the reference object when the observer faces the encoded orientation. If the observer is asked to imagine facing the Test 1 orientation, which is larger (more positive) tiian the encoded orientation, then the target should be at -95°. If the encoded representation competes with the transformed representation and the response ends up
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Figure 1. The logic of the attraction analysis and the predictions of the four hypotheses of spatial representations for the saw-tooth performance. Panel a illustrates a target's direction relative to the reference object in the encoded representation (-50°) and in two examples of transformed representations (-95° and -35°) (top portion), and a schematic function of the signed errors relative to the imagined orientations (bottom portion). Panel b illustrates the predicted attraction effects for the four-orientation hypothesis, one-axis hypothesis, one-orientation hypothesis, and orientation-invariant hypothesis, respectively, from top to bottom.
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being a compromise between the two (e.g., -70°), then there is a positive bias of 25° (i.e., [-70] - [-95] = 25). Similarly, if the observer is asked to imagine facing Test 2 orientation, which is smaller (more negative) than the encoded orientation, then the target should be at —35°. If there is a compromise between the transformed representation and the original encoded representation, the response would be somewhere in between (e.g., —45°). As a result, there is a negative bias of 10° (i.e., [-45] - [-35] = -10). In general, there should be positive biases for imagined orientations larger than the encoded orientation and negative biases for imagined orientations smaller than the encoded orientation. Moreover, the size of the bias may increase as the imagined orientation deviates from the encoded orientation, up to a turning point. Because the biased response is intermediate between the encoded representation and the transformed representation, the size of the bias cannot exceed the angle between the imagined orientation and the encoded orientation. For example, the angle between Test 1 orientation and the encoded orientation is 45° (see Figure la, top portion). According to the competition model, the response of the target direction while imagining facing Test 1 may be between -95° (no attraction by the encoded representation) and -50° (completely attracted to the encoded representation). Accordingly, the bias may range from 0° to 45°, which is no more than the angle between Test 1 and the encoded orientation. Due to this upper bound limit, the response bias has to be small when the imagined orientation is very close to the encoded orientation. When the imagined orientation deviates more from the encoded orientation, there is more room for larger biases. Thus, the size of the biases may increase as the imagined rotation becomes larger (see Figure la, bottom portion). This trend cannot go on forever, however, because of the circular nature of imagined rotations. For example, the 180° rotation is the same imagined orientation as the -180° rotation; therefore, the size of the biases may not increase beyond imagined rotations of 180° and -180°. Similarly, when there are multiple encoded orientations, the biases cannot keep getting larger when the imagined orientation deviates from one encoded representation, because it will eventually get closer to the adjacent encoded representation. Therefore, the bias may increase in size as the imagined orientation deviates from the encoded orientation up to some angle, after which the size of the bias may start to decrease. The above analyses suggest that the competition model predicts a positive correlation between the signed error and the imagined orientation around the encoded orientation. This attraction effect does not occur for the transient transformed representations, and therefore may be used to differentiate spatial representations and spatial transformations. However, this positive correlation only applies to test orientations near the encoded representations. The competition model does not make a priori predictions about the exact shape of the overall function and its parameters, such as the magnitude of the attraction, the location of the peaks/tuming points, the steepness of the slope, and, in case of multiple encoded representations, what the function is like at the boundary between adjacent encoded orientations. In the present experiment, we examined the spatial representations for regular object layouts with salient, coherent directional cues in the environment and in explicit instructions using the proposed attraction analysis paradigm. It has been shown that JRD performance was better in fotir orientations aligned with the main axis under such
experimental conditions (Mou & McNamara, 2002). However, there are at least four plausible interpretations of these findings. First, all four orientations were represented (i.e., the traditional interpretation based on the performance analysis). Second, only the main axis (both directions) was represented, whereas advantages for the other axis were due to transformations. Third, only one orientation was represented, whereas the other three orthogonal orientations were due to transformations. Fourth, the representation is orientation-invariant, and the advantages of all four orientations were due to transformations (see Figure lb). We sought to differentiate among these four potential interpretations by examining which of the four preferred orientations show an attraction effect.
Method Participants Twenty-five students from the University of Illinois at UrbanaChampaign psychology subject pool participated in the experiment. Each participant received course credit for their participation.
Apparatus The experiment was conducted in a rectangular room measuring 6.7 m X 4.3 m. A rectangular mat (1.8 m X 1.1m) was placed on the floor in the middle of the room. Seven ordinary objects were placed on the mat, forming a regular pattem (see Figure 2, top panel). The object array configuration was constructed according to the display used by Mou and McNamara (2002). The long axes of the room and the mat, and the symmetry axis of the object array, were aligned (the main axis). Participants sat near one comer of the mat facing the center of the object array. The facing direction was —45° from tbe main axis.
Procedure The experiment was divided into a leaming stage and a testing stage. During the leaming stage, participants were led with their eyes closed to a chair at the studying position facing the center of the object array. They were instructed to memorize the location of the objects from the indicated direction (hereafter referred to as the 0° orientation). They studied the array for 30 s and then were tested on the location of each object as if they were facing the 0°. ' If needed, they repeated another 30 s of study and test until they remembered all seven objects accurately. After the participant demonstrated accurate knowledge of all the object locations, they were led out of tbe room with their eyes closed to another room where they made judgments of relative directions on a computer. In this testing stage, each participant completed 160 trials. In each trial, the name of one object appeared in the center of tbe monitor, another name right above it, and a third name, controlled
' Participants were asked to point to the targets one by one in any order they like, as if they were "drawing" a map of the array in front of them with their fmger. Their responses were considered correct if all objects were placed at the appropriate positions on a 3 x 3 grid, as judged visually by the experimenter. Their memories were further verified by map drawing after the test session.
SPATIAL MEMORY AND SPATIAL TRANSFORMATIONS
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Data Analysis Participants were first screened according to their map drawing by two criteria: (a) drew all target locations correctiy and (b) spontaneously drew the map oriented with the jar at the top to ensure that they memorized the array from the direction instmcted. All participants met the criteria and were included in the analysis. Two analyses were conducted. First, performance measured as accuracy (absolute angular errors) and response time were examined as a ñanction of the imagined heading orientation. On the basis of previous research (Mou & McNamara, 2002), it was expected that performance should show a "saw-tooth" pattem, with better performance (lower absolute error and response time) for the aligned orientations (0°, 90°, -90°, 180°) than the misaligned orientations. Second, the signed errors (the response angle minus the correct angle) were examined as a function of the imagined headings. To test whether each of the four aligned orientations were encoded in the original representation, a linear regression was mn on the signed errors as a function of the imagined heading for each of the aligned orientations (0°, 90°, -90°, 180°) within a range of ± 45°.^ A positive slope would suggest that the orientation was represented (see Figure lb).
Results
Figure 2. A snapshot of the experimental setup taken from the viewpoint of the participants during the learning stage (top panel). Participants were instructed to memorize the object locations as if they were looking at the array along a direction indicated by the arrow (cf. Mou & McNamara, 2002). The bottom panel shows a sample test display (i.e., imagine standing at the Pot, facing the Brush, point to the Basket). The arrows were for illustration only and were not in the test display.
by the mouse, could be moved along an invisible circle centered at tiie central object name (see Figure 2, bottom panel). Participants were instmcted to imagine being in the study room standing at the center object, facing the top object, and to move the third object to indicate the appropriate direction and click the mouse button. Both the response direction and tiie RTs were recorded. After the response, the object names disappeared, and the next trial began after a 1-s delay. The three testing objects were randomly selected. For each trial, a reference object was randomly selected among the seven objects, then the facing object was randomly selected from the remaining six objects. Finally, the pointing target was randomly selected from the remaining five objects. There were totally 16 different imagined heading orientations. After completing all the testing trials, the participants were given a sheet of paper and asked to draw a map of the object layout.
Trials with absolute errors larger than 90° were considered mistakes and were excluded from the analyses. Overall, 462 trials were excluded (12%). The performance data replicated previous research and showed a saw-tooth pattem, with lower response time, paired f(24) = 4.4, p < .001, d = .87, and absolute errors, paired f(24) = 7.2, p < .001, d = 1.44, at the aligned orientations than the misaligned orientations (see Figure 3a and 3b). These results suggested that based on the performance measure, there were four preferred orientations (0°, 90°, -90°, 180°).^ To examine whether each of these preferred orientations refiects spatial representations or spatial transformations, an attraction analysis was conducted (see Figure 3c). There was a positive correlation between the signed errors and the imagined orientation in tiie quadrant centered around 0° {r = .55, p < .001) but not those around 90°, -90°, and 180° (rs < .1 l,ps > .27)." These data
^The imagined orientations between (-180°, -135°) were recoded to (180°, 225°) for the analysis of 180°. ^ There was a significant difference in absolute errors among the four preferred orientations, F(3, 72) = 3.1, p < .05, but not in the RTs, F(3, 72) = 1.4, p = .25. Note that performance difference could occur between multiple represented perspectives with different quality/strength; therefore, it does not by itself provide evidence against the traditional interpretations. " The signed error for each imagined orientation was averaged across various target directions. Thus, biases due to different target directions (e.g., targets in front vs. behind) should in general cancel each other out, and the average bias should primarily reflect the effects of imagined orientations. To further control for the effects of target directions, an additional attraction analysis was conducted using only target directions within 45° of each imagined orientation, that is, using roughly the same target directions for all imagined headings so that variations in the biases should be primarily due to different imagined heading, not different target directions. The linear regression results were comparable to the full targetset data, with significant positive correlation for 0° (r = .38, p < .001) but not for the other three orientations (rs < .05, ps > .14).
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Test orientation Figure 3. Results of (a) response time, (b) absolute errors, and (c) signed errors as a function of the test orientations. The error bars show ± 1 standard error of the mean. RT = response time; deg = degrees.
were consistent with the one-orientation hypothesis that only the 0° orientation was represented in memory, whereas the good performance for the other three preferred orientations was due to transformation advantages.
Discussion Conventional perspective change paradigms usually rely on performance as the indicator of the underlying spatial representations. However, good performance could also be due to relative ease in certain spatial transformations. To distinguish between these possibilities, an attraction analysis was developed based on a competition model. This new approach was applied to a perspective-taking task using regular arrays. Following the procedure of Mou and McManara (2002), participants memorized an array of objects and performed JRD tests. Performance (RT and accuracy) of the JRD task replicated previous findings, showing a saw-tooth pattern with best performance in the four aligned orientations, which is generally interpreted as spatial memory encoding all four orientations. However, the attraction analysis showed
attraction effects toward the 0° orientation but not toward the other three preferred orientations. These data supported the hypothesis that only one orientation was represented in memory, and better performance at the other three preferred orientations was due to transformation advantages. These findings demonstrated that the attraction analysis can be used to distinguish between effects of spatial representations and spatial transformations. This new paradigm appears more sensitive than the traditional performance analysis. That is, the performance data showed advantages for four orthogonal orientations, which were consistent with at least four plausible interpretations of spatial representations: (a) All four orientations were represented in spatial memory; (b) one axis (both directions) was represented in memory; (c) only one orientation was represented in memory; (d) the memory itself was orientation-invariant and had no preferred orientation. In contrast, the attraction analysis showed different patterns for the four orientations, with the attraction effect present for the 0° orientation only. Thus, the attraction analysis was able to eliminate the three alternative possibilities and provide
SPATIAL MEMORY AND SPATIAL TRANSFORMATIONS
support for orientation-specific spatial representation from a single orientation. These findings further suggested that precautions need to be taken when interpreting performance data in perspective change tasks. The traditional perspective change paradigm can potentially mistaken effects of transformations as effects of spatial encoding. For example, according to the traditional approach, all four reference directions were selected in spatial memory (Mou & McNamara, 2002). However, the attraction analysis casted doubt on such interpretations and suggested that these performance advantages were due to different mechanisms. Our study raised a number of interesting questions. First, the present data showed that people only represented the object array along a single orientation aligned with the main axis of the array/ room. This finding may be specific to the experimental condition and may not generalize to other conditions (e.g., with irregular arrays, with different instmctions, with different environmental cues, with more familiar environments, etc.). Second, the attraction effect was apparently due to the competition between information in the original representation and that in the transformed representation. However, the exact locus of the competition is unknown. The competition may occur at the representation level, or it may occur at the response level, or both. Third, the exact cause for the transformation advantage is still unclear. Possible factors include the type of transformations (e.g., ortiiogonal better than nonorthogonal), the stability of the resulting representations (e.g., symmetrical/colinearity better than random), and so on. These issues await future investigations. Another important question concems the nature of the competition process. There are at least two possible mechanisms by which the encoded representation may compete with the transformed representation for locating a target from an imagined orientation. First, each response may be the weighted average of the target direction relative to the encoded orientation and that relative to the imagined orientation. Second, each response may be made either according to the transformed representation or according to the original encoded representation, and each representation may be selected for the response with a certain probability. Responses based on such a selection probability mechanism will result in an overall mean response somewhere in between. Both mechanisms are consistent with the attraction analysis data. However, they make different predictions about the distribution of the biases. The weighted average mechanism predicts a single peak distribution, whereas the selection probability mechanism predicts a two-peak distribution, with one peak centered at 0°, which corresponds to the trials using the transformed representation and therefore having no bias, and another peak that corresponds to the trials using the original encoded representation. Ongoing research is developing a new distribution analysis to examine these mechanisms. In summary, the attraction analysis showed that under the experimental conditions used in the present study, people form orientation-dependent spatial representation of a regular object layout only along one orientation even though their performance showed advantages for four orthogonal orientations. These findings challenged the traditional performance-based theories of perspective change processes and suggested that interpretations of spatial representations based on performance analysis in perspective change paradigms need to be revisited.
607 References
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Received March 5, 2013 Revision received October 9, 2013 Accepted October II, 2013
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Joumal of Experimental Psychology: Leaming, Memory, and Cognition 2014, Vol. 40. No. 2, 602-608
RESEARCH REPORT
Differentiating Spatial Memory From Spatial Transformations Whitney N. Street and Ranxiao Frances Wang University of IlUnois at Urbana-Champaign The perspective-taking task is one of the most common paradigms used to study the nature of spatial memory, and better performance for certain orientations is generally interpreted as evidence of spatial representations using these reference directions. However, performance advantages can also result from the relative ease in certain transformations/rotations. To differentiate spatial memory from spatial transformations, the present study took a new approach based on the hypothesis that responses may be biased toward the original representation but not a transformed one. Participants memorized a regular target array and then judged the relative direction between 2 targets while imagining facing various directions. Their response time and absolute errors showed the standard advantages at 4 imagined orientations. In contrast, an attraction analysis suggested that only 1 orientation was represented in memory, whereas performance advantages at other orthogonal orientations were due to lower transformation costs and should not be interpreted as spatial representations. These findings challenged the traditional performance-based interpretations of perspective change tasks and provided a new research paradigm to differentiate spatial representations from spatial transformations. Keyword^: spatial representation, reference frame, perspective taking, spatial transformation
require less response time and lead to higher accuracy (Mou & McNamara, 2002; Rieser, 1989; Shelton & McNamara, 2001; Simons & Wang, 1998; Waller, 2006; Waller, Montello, Richardson, & Hegariy, 2002; Wang, 2007). As intuitive as this paradigm is, it has a major theoretical limitation. Performance in a perspective change task can refiect the nature of the spatial memory, the efficiency of the spatial transformation/spatial reasoning processes, or both. This limitation is particularly prominent when performance advantages are shown for multiple orientations (e.g., Kelly & Avraamides, 2011; Liu, Mou, & McNamara, 2011; Mou & McNamara, 2002). For example. Mou and McNamara (2002) asked participants to memorize a set of objects and make judgments of relative directions (JRD) among them (e.g., imagine you are at X, facing Y, point to Z). They showed that performance was better when the imagined heading was either parallel with or orthogonal to the axis of the layout (the "alignment effect"), thus showing a "saw-tooth" pattern in response time (RT)/accuracy as a function of the imagined heading. According to the traditional performance-advantage hypothesis, these data provide evidence that four reference directions were used in encoding spatial relations among the objects, and misaligned perspectives were transformed from these representations. However, there are at least two alternative hypotheses. First, spatial information might be coded relative to a reference axis (including both directions, e.g., 0° and 180°), whereas performance advantages for directions orihogonal to that axis (e.g., 90° and 270°) was due to minimal cost in making orthogonal transformations. Second, it is also possible that only a single reference direction was used to encode spatial information (e.g., 0° only), and imagined heading along all other directions were inferred from this
Spatial memory is an important cognitive function that is shared by most animal species. Extensive research has been devoted to studying the nature of spatial representations in insects, birds, and mammals, including humans, using various research paradigms such as the novel shortcut tests (e.g., Bennett, 1996; Foo, Warren, Duchon, & Tarr, 2005; Tolman, 1948), landmark/cue manipulations (e.g.. Burgess, 2006; Burgess, Spiers, & Paleologou, 2004; CoUett & Cartwright, 1983; Collett & Rees, 1997; O'Keefe & Speakman, 1987), disorientations (Hermer & Spelke, 1996; Learmonth, Newcombe, & Huttenlocher, 2001; Wang, 2012; Wang & Spelke, 2000, 2002), and so on. Among these paradigms, the perspective change task is one of the most widely used methods in studying human spatial representations. In a typical task, participants leam a set of targets in an environment. They are then asked to make judgments of spatial relations from various perspectives. Performance is taken as an indicator of the underlying representations based on the hypothesis that encoded perspectives are directly retrieved; therefore, they
This article was published Online First December 23, 2013. Whitney N. Street and Ranxiao Frances Wang, Department of Psychology, University of Illinois at Urbana-Champaign. Some of the findings were presented at the 53rd annual meeting of the Psychonomic Society, November 15-18, 2012, Minneapolis, Minnesota. Thanks to Aaron Nachsin, Maria Scheet, Lisa Hutcheson, Anthony Lupo, Shea Kaelin, Juliya Kulbachenko, and Jeremiah Pickert for help with data collection. Correspondence concerning this article should be addressed to Ranxiao Frances Wang, Room 533, Department of Psychology, University of Illinois at Urbana-Champaign, 603 East Daniel Street, Champaign, IL 61820. E-mail: franceswiâ'cyrus.psych.illinois.edu 602
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original representation by spatial transformations. Good performance for the encoded orientation was a result of direct access, whereas good performance for the other three orthogonal orientations refiected efficient spatial transformations for these special angles. The potential confound between spatial representations and spatial transformations exists even when there is only a single preferred orientation (e.g., Rieser, 1989; Shelton & McNamara, 2001; Waller, 2006; Wang, 2007). For example, Shelton and McNamara (2001) showed that when participants leamed an array from multiple directions, performance was best at the leaming direction aligned with the room geometry. These results were usually interpreted as a single orientation-specific representation encoded along the preferred direction. However, it is also possible that the spatial representation itself was orientation-invariant, whereas the performance advantage was caused by the relative ease in reconstructing a mental image of the array from certain orientations due to factors such as symmetry and colinearity. It is vital to distinguish between spatial representations and spatial transformations. However, existing research paradigms based on performance analysis cannot differentiate effects caused by spatial encoding from those caused by the spatial reasoning processes. To address this issue, we took a new approach based on a competition model inspired by previous research on systematic biases in spatial memory (e.g., Huttenlocher, Hedges, & Duncan, 1991; Sampaio & Wang, 2009) and the interference theory of the angular disparity effect (Brockmole & Wang, 2003; May, 2004; Presson, 1982; Wang, 2004, 2005). The competition model assumes that spatial information is encoded in an original represen-
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tation(s). When a task can be solved by directly retrieving information from the original representations (e.g., imagining a perspective coinciding with the encoded one), the original representation is retrieved for the responses. When a task requires spatial information that is not contained in the original representation, spatial transformation is performed to generate a new representation (e.g., imagining what a scene is like from a novel perspective), which is then used to perform the task. However, because there is a discrepancy between the information in the original representation and that in the transformed representation, the original representation may compete with the transformed representation, causing the responses to be biased toward the original representation. On the contrary, the transformed representations are transient and generated only for the current response. Therefore, they should not affect other transformed representations. Finally, when there are multiple encoded representations, the responses should be biased toward the nearest encoded representation. According to this competition model, encoded and transformed representations may be differentiated by examining the attraction effects in the biases. Figure la illustrates the logic of the attraction effect of an encoded representation on the transformed representations. The top portion shows an example of one target at -50° from the reference object when the observer faces the encoded orientation. If the observer is asked to imagine facing the Test 1 orientation, which is larger (more positive) tiian the encoded orientation, then the target should be at -95°. If the encoded representation competes with the transformed representation and the response ends up
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Figure 1. The logic of the attraction analysis and the predictions of the four hypotheses of spatial representations for the saw-tooth performance. Panel a illustrates a target's direction relative to the reference object in the encoded representation (-50°) and in two examples of transformed representations (-95° and -35°) (top portion), and a schematic function of the signed errors relative to the imagined orientations (bottom portion). Panel b illustrates the predicted attraction effects for the four-orientation hypothesis, one-axis hypothesis, one-orientation hypothesis, and orientation-invariant hypothesis, respectively, from top to bottom.
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being a compromise between the two (e.g., -70°), then there is a positive bias of 25° (i.e., [-70] - [-95] = 25). Similarly, if the observer is asked to imagine facing Test 2 orientation, which is smaller (more negative) than the encoded orientation, then the target should be at —35°. If there is a compromise between the transformed representation and the original encoded representation, the response would be somewhere in between (e.g., —45°). As a result, there is a negative bias of 10° (i.e., [-45] - [-35] = -10). In general, there should be positive biases for imagined orientations larger than the encoded orientation and negative biases for imagined orientations smaller than the encoded orientation. Moreover, the size of the bias may increase as the imagined orientation deviates from the encoded orientation, up to a turning point. Because the biased response is intermediate between the encoded representation and the transformed representation, the size of the bias cannot exceed the angle between the imagined orientation and the encoded orientation. For example, the angle between Test 1 orientation and the encoded orientation is 45° (see Figure la, top portion). According to the competition model, the response of the target direction while imagining facing Test 1 may be between -95° (no attraction by the encoded representation) and -50° (completely attracted to the encoded representation). Accordingly, the bias may range from 0° to 45°, which is no more than the angle between Test 1 and the encoded orientation. Due to this upper bound limit, the response bias has to be small when the imagined orientation is very close to the encoded orientation. When the imagined orientation deviates more from the encoded orientation, there is more room for larger biases. Thus, the size of the biases may increase as the imagined rotation becomes larger (see Figure la, bottom portion). This trend cannot go on forever, however, because of the circular nature of imagined rotations. For example, the 180° rotation is the same imagined orientation as the -180° rotation; therefore, the size of the biases may not increase beyond imagined rotations of 180° and -180°. Similarly, when there are multiple encoded orientations, the biases cannot keep getting larger when the imagined orientation deviates from one encoded representation, because it will eventually get closer to the adjacent encoded representation. Therefore, the bias may increase in size as the imagined orientation deviates from the encoded orientation up to some angle, after which the size of the bias may start to decrease. The above analyses suggest that the competition model predicts a positive correlation between the signed error and the imagined orientation around the encoded orientation. This attraction effect does not occur for the transient transformed representations, and therefore may be used to differentiate spatial representations and spatial transformations. However, this positive correlation only applies to test orientations near the encoded representations. The competition model does not make a priori predictions about the exact shape of the overall function and its parameters, such as the magnitude of the attraction, the location of the peaks/tuming points, the steepness of the slope, and, in case of multiple encoded representations, what the function is like at the boundary between adjacent encoded orientations. In the present experiment, we examined the spatial representations for regular object layouts with salient, coherent directional cues in the environment and in explicit instructions using the proposed attraction analysis paradigm. It has been shown that JRD performance was better in fotir orientations aligned with the main axis under such
experimental conditions (Mou & McNamara, 2002). However, there are at least four plausible interpretations of these findings. First, all four orientations were represented (i.e., the traditional interpretation based on the performance analysis). Second, only the main axis (both directions) was represented, whereas advantages for the other axis were due to transformations. Third, only one orientation was represented, whereas the other three orthogonal orientations were due to transformations. Fourth, the representation is orientation-invariant, and the advantages of all four orientations were due to transformations (see Figure lb). We sought to differentiate among these four potential interpretations by examining which of the four preferred orientations show an attraction effect.
Method Participants Twenty-five students from the University of Illinois at UrbanaChampaign psychology subject pool participated in the experiment. Each participant received course credit for their participation.
Apparatus The experiment was conducted in a rectangular room measuring 6.7 m X 4.3 m. A rectangular mat (1.8 m X 1.1m) was placed on the floor in the middle of the room. Seven ordinary objects were placed on the mat, forming a regular pattem (see Figure 2, top panel). The object array configuration was constructed according to the display used by Mou and McNamara (2002). The long axes of the room and the mat, and the symmetry axis of the object array, were aligned (the main axis). Participants sat near one comer of the mat facing the center of the object array. The facing direction was —45° from tbe main axis.
Procedure The experiment was divided into a leaming stage and a testing stage. During the leaming stage, participants were led with their eyes closed to a chair at the studying position facing the center of the object array. They were instructed to memorize the location of the objects from the indicated direction (hereafter referred to as the 0° orientation). They studied the array for 30 s and then were tested on the location of each object as if they were facing the 0°. ' If needed, they repeated another 30 s of study and test until they remembered all seven objects accurately. After the participant demonstrated accurate knowledge of all the object locations, they were led out of tbe room with their eyes closed to another room where they made judgments of relative directions on a computer. In this testing stage, each participant completed 160 trials. In each trial, the name of one object appeared in the center of tbe monitor, another name right above it, and a third name, controlled
' Participants were asked to point to the targets one by one in any order they like, as if they were "drawing" a map of the array in front of them with their fmger. Their responses were considered correct if all objects were placed at the appropriate positions on a 3 x 3 grid, as judged visually by the experimenter. Their memories were further verified by map drawing after the test session.
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Data Analysis Participants were first screened according to their map drawing by two criteria: (a) drew all target locations correctiy and (b) spontaneously drew the map oriented with the jar at the top to ensure that they memorized the array from the direction instmcted. All participants met the criteria and were included in the analysis. Two analyses were conducted. First, performance measured as accuracy (absolute angular errors) and response time were examined as a ñanction of the imagined heading orientation. On the basis of previous research (Mou & McNamara, 2002), it was expected that performance should show a "saw-tooth" pattem, with better performance (lower absolute error and response time) for the aligned orientations (0°, 90°, -90°, 180°) than the misaligned orientations. Second, the signed errors (the response angle minus the correct angle) were examined as a function of the imagined headings. To test whether each of the four aligned orientations were encoded in the original representation, a linear regression was mn on the signed errors as a function of the imagined heading for each of the aligned orientations (0°, 90°, -90°, 180°) within a range of ± 45°.^ A positive slope would suggest that the orientation was represented (see Figure lb).
Results
Figure 2. A snapshot of the experimental setup taken from the viewpoint of the participants during the learning stage (top panel). Participants were instructed to memorize the object locations as if they were looking at the array along a direction indicated by the arrow (cf. Mou & McNamara, 2002). The bottom panel shows a sample test display (i.e., imagine standing at the Pot, facing the Brush, point to the Basket). The arrows were for illustration only and were not in the test display.
by the mouse, could be moved along an invisible circle centered at tiie central object name (see Figure 2, bottom panel). Participants were instmcted to imagine being in the study room standing at the center object, facing the top object, and to move the third object to indicate the appropriate direction and click the mouse button. Both the response direction and tiie RTs were recorded. After the response, the object names disappeared, and the next trial began after a 1-s delay. The three testing objects were randomly selected. For each trial, a reference object was randomly selected among the seven objects, then the facing object was randomly selected from the remaining six objects. Finally, the pointing target was randomly selected from the remaining five objects. There were totally 16 different imagined heading orientations. After completing all the testing trials, the participants were given a sheet of paper and asked to draw a map of the object layout.
Trials with absolute errors larger than 90° were considered mistakes and were excluded from the analyses. Overall, 462 trials were excluded (12%). The performance data replicated previous research and showed a saw-tooth pattem, with lower response time, paired f(24) = 4.4, p < .001, d = .87, and absolute errors, paired f(24) = 7.2, p < .001, d = 1.44, at the aligned orientations than the misaligned orientations (see Figure 3a and 3b). These results suggested that based on the performance measure, there were four preferred orientations (0°, 90°, -90°, 180°).^ To examine whether each of these preferred orientations refiects spatial representations or spatial transformations, an attraction analysis was conducted (see Figure 3c). There was a positive correlation between the signed errors and the imagined orientation in tiie quadrant centered around 0° {r = .55, p < .001) but not those around 90°, -90°, and 180° (rs < .1 l,ps > .27)." These data
^The imagined orientations between (-180°, -135°) were recoded to (180°, 225°) for the analysis of 180°. ^ There was a significant difference in absolute errors among the four preferred orientations, F(3, 72) = 3.1, p < .05, but not in the RTs, F(3, 72) = 1.4, p = .25. Note that performance difference could occur between multiple represented perspectives with different quality/strength; therefore, it does not by itself provide evidence against the traditional interpretations. " The signed error for each imagined orientation was averaged across various target directions. Thus, biases due to different target directions (e.g., targets in front vs. behind) should in general cancel each other out, and the average bias should primarily reflect the effects of imagined orientations. To further control for the effects of target directions, an additional attraction analysis was conducted using only target directions within 45° of each imagined orientation, that is, using roughly the same target directions for all imagined headings so that variations in the biases should be primarily due to different imagined heading, not different target directions. The linear regression results were comparable to the full targetset data, with significant positive correlation for 0° (r = .38, p < .001) but not for the other three orientations (rs < .05, ps > .14).
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Test orientation Figure 3. Results of (a) response time, (b) absolute errors, and (c) signed errors as a function of the test orientations. The error bars show ± 1 standard error of the mean. RT = response time; deg = degrees.
were consistent with the one-orientation hypothesis that only the 0° orientation was represented in memory, whereas the good performance for the other three preferred orientations was due to transformation advantages.
Discussion Conventional perspective change paradigms usually rely on performance as the indicator of the underlying spatial representations. However, good performance could also be due to relative ease in certain spatial transformations. To distinguish between these possibilities, an attraction analysis was developed based on a competition model. This new approach was applied to a perspective-taking task using regular arrays. Following the procedure of Mou and McManara (2002), participants memorized an array of objects and performed JRD tests. Performance (RT and accuracy) of the JRD task replicated previous findings, showing a saw-tooth pattern with best performance in the four aligned orientations, which is generally interpreted as spatial memory encoding all four orientations. However, the attraction analysis showed
attraction effects toward the 0° orientation but not toward the other three preferred orientations. These data supported the hypothesis that only one orientation was represented in memory, and better performance at the other three preferred orientations was due to transformation advantages. These findings demonstrated that the attraction analysis can be used to distinguish between effects of spatial representations and spatial transformations. This new paradigm appears more sensitive than the traditional performance analysis. That is, the performance data showed advantages for four orthogonal orientations, which were consistent with at least four plausible interpretations of spatial representations: (a) All four orientations were represented in spatial memory; (b) one axis (both directions) was represented in memory; (c) only one orientation was represented in memory; (d) the memory itself was orientation-invariant and had no preferred orientation. In contrast, the attraction analysis showed different patterns for the four orientations, with the attraction effect present for the 0° orientation only. Thus, the attraction analysis was able to eliminate the three alternative possibilities and provide
SPATIAL MEMORY AND SPATIAL TRANSFORMATIONS
support for orientation-specific spatial representation from a single orientation. These findings further suggested that precautions need to be taken when interpreting performance data in perspective change tasks. The traditional perspective change paradigm can potentially mistaken effects of transformations as effects of spatial encoding. For example, according to the traditional approach, all four reference directions were selected in spatial memory (Mou & McNamara, 2002). However, the attraction analysis casted doubt on such interpretations and suggested that these performance advantages were due to different mechanisms. Our study raised a number of interesting questions. First, the present data showed that people only represented the object array along a single orientation aligned with the main axis of the array/ room. This finding may be specific to the experimental condition and may not generalize to other conditions (e.g., with irregular arrays, with different instmctions, with different environmental cues, with more familiar environments, etc.). Second, the attraction effect was apparently due to the competition between information in the original representation and that in the transformed representation. However, the exact locus of the competition is unknown. The competition may occur at the representation level, or it may occur at the response level, or both. Third, the exact cause for the transformation advantage is still unclear. Possible factors include the type of transformations (e.g., ortiiogonal better than nonorthogonal), the stability of the resulting representations (e.g., symmetrical/colinearity better than random), and so on. These issues await future investigations. Another important question concems the nature of the competition process. There are at least two possible mechanisms by which the encoded representation may compete with the transformed representation for locating a target from an imagined orientation. First, each response may be the weighted average of the target direction relative to the encoded orientation and that relative to the imagined orientation. Second, each response may be made either according to the transformed representation or according to the original encoded representation, and each representation may be selected for the response with a certain probability. Responses based on such a selection probability mechanism will result in an overall mean response somewhere in between. Both mechanisms are consistent with the attraction analysis data. However, they make different predictions about the distribution of the biases. The weighted average mechanism predicts a single peak distribution, whereas the selection probability mechanism predicts a two-peak distribution, with one peak centered at 0°, which corresponds to the trials using the transformed representation and therefore having no bias, and another peak that corresponds to the trials using the original encoded representation. Ongoing research is developing a new distribution analysis to examine these mechanisms. In summary, the attraction analysis showed that under the experimental conditions used in the present study, people form orientation-dependent spatial representation of a regular object layout only along one orientation even though their performance showed advantages for four orthogonal orientations. These findings challenged the traditional performance-based theories of perspective change processes and suggested that interpretations of spatial representations based on performance analysis in perspective change paradigms need to be revisited.
607 References
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Received March 5, 2013 Revision received October 9, 2013 Accepted October II, 2013
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