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Differential strategy use is a topic of intense investigation in developmental psychology. Questions under study are as follows: How do strategies change with age, how can individual differences in strategy use be explained, and which interventions promote shifts from suboptimal to optimal strategies? In order to detect such differential strategy use, developmental psychology currently relies on two approaches—the rule assessment methodology and latent class analysis—each having their own strengths and weaknesses. In order to optimize strategy detection, a new approach that combines the strengths of both existing methods and avoids their weaknesses was recently developed: model-based latent-mixture analysis using Bayesian inference. We performed a simulation study to test the ability of this new approach to detect differential strategy use. Next, we illustrate the benefits of this approach by a re-analysis of decision making data from 210 children and adolescents. We conclude that the new approach yields highly informative results, and provides an adequate account of the observed data. To facilitate the application of this new approach in other studies, we provide open access documented code, and a step-by-step tutorial of its usage.
The concept of differential strategy use is ubiquitous in developmental psychology. A first line of developmental research focuses on whether strategy use changes with age. For example, a young child having to add three and four may count to three and then count four further, whereas an older child might retrieve the answer from memory (Ashcraft and Fierman 1982). There is thus a developmental shift in strategy use: from a counting strategy to a retrieval strategy. Such developmental shifts in strategy use have been reported in a variety of domains, for example in decision making (Aïte et al. 2012; Bereby-meyer et al. 2004; Betsch and Lang 2013; Huizenga et al. 2007; Jacobs and Potenza 1991; Jansen et al. 2012; Kwak et al. 2015; Lang and Betsch 2018; Reyna 2008; Schlottmann 2001, 2000; Schlottmann and Anderson 1994), reasoning (Bouwmeester and Sijtsma 2007; Bouwmeester et al. 2004; Houdé et al. 2011; Jansen and van der Maas 2001, 2002; Siegler 1987, 2007; Siegler et al. 1981; van der Maas and Molenaar 1992; Wilkening 1981), reinforcement learning (Andersen et al. 2014; Decker et al. 2016; Palminteri et al. 2016; Potter et al. 2017; Schmittmann et al. 2012; Schmittmann et al. 2006), mathematics (Ashcraft and Fierman 1982; Bjorklund and Rosenblum 2001; Cho et al. 2011; Torbeyns et al. 2009), and categorization (Rabi et al. 2015; Raijmakers et al. 2004). A second line of research focuses on individual differences in strategy use within age groups (Siegler 1988), which have been shown to depend on variables such as intelligence (Bexkens et al. 2016) and the capacity to inhibit (Borst et al. 2012; Poirel et al. 2012). Finally, a third line of developmental research examines the effects of interventions aimed at changing children's or adolescents' suboptimal strategies into optimal ones (Alibali 1999; Felton 2004; Perry et al. 2010; Stevenson et al. 2016). For these three types of developmental questions, it is important to detect differential strategy use adequately. Hence, the goal of this paper is to describe an adequate method to detect differential strategy use, which can easily be used by developmental psychologists.
An example of a paradigm in which strategy use is crucial is the balance scale task (e.g., Siegler and Chen 2002). In this task, participants have to decide whether a balance will tip, and if so, to which side (cf. Fig. 1). Many strategies can be used to solve this task. For example, some participants, using the optimal strategy, decide given the number of weights multiplied by their distance to the fulcrum. Other participants, using a suboptimal strategy, decide given the number of weights only. Still, other participants use another suboptimal strategy, in which they decide given the number of weights if weight differences are present, and decide given distance if weight differences are absent. Note that the particular item in Fig. 1 does not differentiate between the latter two suboptimal strategies, as they will give rise to the same answer ("right"). Therefore, studies investigating strategy use typically administer not only a single item, but a set of items. In a fictitious eight item example, the response pattern of a single participant may be "right, balance, balance, right, left, right, left, right." The response patterns of multiple participants are then input to analyses aimed at detecting strategy use.
In developmental psychology, one approach to detect strategy use is the rule-assessment methodology (Siegler 1976; Siegler et al. 1981). According to this method, a participant is assigned to a particular strategy ("rule"), if the proportion of observed responses consistent with the predicted responses of that strategy exceeds a cut-off value. In the balance scale example, the observed response pattern ("right, balance, balance, right, left, right, left, right") and predicted response pattern (e.g., "left, balance, balance, right, right, right, left, right") match six out of eight (75%) responses. If the cut-off value was set at 70%, it thus is decided that this participant uses this particular strategy.
An advantage of the rule assessment methodology is that it is a one-step approach: Strategy use is inferred immediately (Table 1). Another advantage is that it can be used for small samples; even if only one child is tested, their strategy can, in principle, be inferred. However, there are also disadvantages. First, it does not account for error responses. That is, participants may not always make the response predicted by their strategy but may sometimes deviate from it, for example due to lapses of attention or premature responding. This can make strategy assignment difficult. Second, the approach only allows for discrete strategy assignment: A participant is assigned to one strategy and not to others, which might be problematic if the fit to several strategies is approximately equal. Last but not least, the cut-off value (e.g., 70%) is arbitrary; hence, strategy assessment may change if the cut-off value is changed. For these reasons, it has been argued that this methodology may result in spurious detection of strategies (Jansen and van der Maas 2002; Thomas and Horton 1997; van der Maas and Straatemeier 2008; Wilkening 1988).
An alternative approach is based on latent-class analysis (also called latent-mixture analysis; Bouwmeester and Sijtsma 2007; Bouwmeester and Verkoeijen 2012; Hickendorff et al. 2018; Huizenga et al. 2007; Jansen and van der Maas 2002; Nylund et al. 2007a). Although latent class analysis can be used in a confirmatory way, the exploratory way is more common. In this type of latent class analysis, participants are classified into several latent groups, based on similarity in observed response patterns. The number of latent groups required to describe the data is typically determined using penalized information criteria, such as the Bayesian Information Criterion (Schwartz 1978). Once the latent groups have been determined, the researcher evaluates the average response pattern in each latent group, comes up with a strategy that could explain this pattern, and assumes that all participants in that group used that strategy. If different possible strategies are specified beforehand, researchers can also compare the average response pattern in each latent group to the response pattern predicted by each of the pre-specified strategies, for example by computing the Euclidean distance between observed and predicted response patterns. The strategy that best fits the average response pattern of a latent group is then assigned to all participants in that group (Jansen et al. 2012).
The latent-class analysis approach has several advantages. A first advantage is that strategies are identified for average response patterns within subgroups of participants. As average response patterns are affected less by error responses than individual ones, this may benefit adequate strategy assessment. A second advantage is that—in contrast to the rule-assessment methodology—strategy assignment does not depend on an arbitrary criterion. Third, although participants are generally assigned to their most likely latent group, a posteriori probabilities offer the opportunity to identify each individual's likelihood that they belong to each of the latent groups. Finally, as latent-class analysis does not require the specification of possible strategies beforehand, it is an ideal method when studying phenomena in which the number and nature of potential strategies are largely unknown, as in exploratory studies. There are also, however, disadvantages. First, latent-class analysis is a two-step procedure: Instead of directly defining subgroups in terms of common strategy use, it defines subgroups in terms of homogeneous response patterns, and the researcher subsequently assigns the most likely strategy to each subgroup. Second, it uses model selection criteria that have been criticized for not adequately accounting for model complexity (Burnham and Anderson 2002). Third, it does not account for individual differences in error rate. Fourth, it requires large sample sizes to guarantee stable solutions (Jaki et al. in press; Nylund et al. 2007b).
The goal of the current article is to introduce a recently developed alternative approach that is based on the advantages of both the rule assessment and the latent-class analysis methodologies while avoiding their disadvantages: a latent-mixture model implemented in a Bayesian framework (Lee and Sarnecka 2011; Lee 2016; Lee 2018a). Like the rule assessment method, latent-mixture models directly define groups in terms of common strategy use and can be used for any sample size. Furthermore, similar to latent-class analysis, this approach infers the likelihood that each participant uses each of the assumed strategies. Thus, it can simultaneously infer the number and size of strategy groups, each individual participant's group membership, and the certainty of each participant's group membership (Bröder and Schiffer 2003; Lee 2016). In addition, latent-mixture models provide an estimate of how accurately participants follow their inferred strategy, by explicitly formalizing individual differences in error rate. Finally, all conclusions are obtained using Bayesian inference, which quantifies uncertainty about parameters in terms of probability distributions, controls for all aspects of model complexity, and handles missing data in a comprehensive model-based way (e.g., Andrews and Baguley 2013; Bayarri et al. 2016; Lee and Wagenmakers 2005; Wagenmakers 2007; Wetzels et al. 2011, for an introduction to the use and advantages of Bayesian methods in the psychological sciences, see Lee 2018b; Lee and Wagenmakers 2013; Vandekerckhove et al. 2018; Wagenmakers et al. 2016).
Here, we apply the latent-mixture approach, implemented in a Bayesian framework, to infer differential strategy use on a previously established decision-making task, the "Gambling-Machine Task" (Jansen et al. 2012). In the remainder of this article, we first describe the Gambling-Machine Task and various strategies that can be used to perform this task. Next, we describe the latent-mixture model and its implementation in a Bayesian framework, and assess its capacity to recover strategy-use parameters by applying it to generated data. Then, we apply the latent mixture model to Gambling-Machine Task data from 210 children and adolescents (Jansen et al. 2012). In the final section, we discuss our results and their ramifications.
The Gambling-Machine Task
The Gambling-Machine Task (Jansen et al. 2012) is a paper-and-pencil decision-making task in which participants choose between two gambling machines (i.e., a specific Machine A and a specific Machine B that together represent one of the 28 items of the task; an example trial is shown in Fig. 2). Each machine contains 10 balls. Each ball is associated with a specific reward that is printed on the left corner of each machine (i.e., +2 for Machine A and + 4 for Machine B in Fig. 2). In addition, some balls, the gray shaded so-called loss balls, are associated with an additional loss—the exact amount is printed on the balls (i.e., − 10 for both machines in Fig. 2). The two machines of each item differ in at least one of three overtly presented cues: the reward associated with each ball (certain gain; CG), the proportion of loss balls (frequency of loss; FL; 0.1 for Machine A and 0.5 for Machine B in Fig. 2), and the amount of loss associated with each loss ball (AL). On each trial, participants have to indicate whether Machine A or Machine B is more profitable, or whether it does not matter. The correct answer is the option with the highest expected value (with expected value = CG + AL × FL).
The task is based on seven item types, each of which has four versions. The seven item types consist of three simple item types in which the machines differ in only one cue, and four complex item types in which the machines differ in at least two cues that produce a conflict. The different versions of each item type are obtained by slightly adapting the specific amounts of CG, AL, or FL, and by changing the position of Machine A and Machine B.
Decision Strategies
We assume that participants use one of 17 strategies to complete the Gambling-Machine Task (Table 2, first two columns). These strategies cover a guessing strategy, an integrative strategy focusing on the expected value of the machines, and 15 non-compensatory strategies based on take-the-best strategies (Bröder 2000). The guessing strategy assumes that participants randomly choose one of the two machines without considering any of their cues, such that on each trial, the answers "Machine A" and "Machine B" are equally likely. It is assumed that, when guessing, participants will never consider the response "does not matter." The integrative strategy assumes that participants correctly integrate all relevant cues by computing the expected value of each machine and subsequently choose the machine with the highest expected value; if both machines have the same expected value, the option "Does not matter" is chosen. Thus, when following the integrative strategy, the correct answer is always given.
Non-compensatory strategies, such as take-the-best strategies, on the other hand, are sequential strategies that differ in the number of cues that are considered (i.e., the complexity) and the order in which the cues are considered (i.e., the saliency of the cues). According to one-dimensional take-the-best strategies, participants compare the options on only one cue, say FL. If the machines differ on FL, the machine with the lowest FL is chosen; otherwise, the answer "Does not matter" is given. According to two-dimensional take-the-best strategies, the machines are sequentially compared on the two most salient cues, say FL and AL. The second, less salient, cue is only considered if the machines do not differ on the first cue. If the machines do not differ on either of the two cues, the answer "Does not matter" is given. The three-dimensional strategies work analogously. We obtain 15 possible take-the-best strategies as the result of all combinations of the three cues, while allowing to sequentially consider either one, two, or three cues (Table 2).
These 17 strategies predict distinctive response patterns that are deterministic for all but the guessing strategy. Thus, a participant's answers to the Gambling-Machine Task items can be used to infer which of the 17 strategies the participant used. To accomplish this, we use a latent-mixture model implemented in a Bayesian framework.
The Latent-Mixture Model
The latent-mixture approach assumes that each individual uses one of the 17 decision strategies, such that the overall data set reflects a mixture of these specific strategies. Figure 3 shows a graphical representation of our model. The nodes stand for model variables and data, and the arrows indicate how the model variables are assumed to generate the data. Square nodes represent discrete variables and round nodes represent continuous variables. Nodes are shaded when the corresponding variables are observed but are unshaded when the variables are latent or unknown. Nodes with double borders indicate deterministic variables. The plates show independent repetitions in the graph structure across all items and participants.
The data yi,q are participants' answers to the Gambling-Machine Task items, with i referring to a specific participant and q to one of the 28 items; yi,q can be either "A" (Machine A), "B" (Machine B), or "DM" (Does not matter). The data are represented by a shaded, square node because they are observed, discrete choices.
The model assumes that each participant's data is generated by one of the 17 strategies. The specific strategy used by participant i is indicated by the latent categorical variable zi, which can take one out of 17 values. Note that zi is represented by an unshaded, square node because it is latent and discrete. All of the strategies, except for the guessing strategy, generate deterministic predictions of participants' answers to each item. These predictions are denoted by ti,q. The predictions depend on the cues of item q (i.e., the machines' certain gain, amount of loss, and frequency of loss) which are labeled as sq. To account for possible deviations from the deterministic predictions, the model assumes that each participant has an individual error rate ∈i (Rieskamp 2008) that is used to convert the predictions into answer probabilities pi,q. Specifically, each participant chooses the option predicted by his/her strategy with probability 1–2∈i, and each of the two remaining options with a probability of ∈i. Thus, the higher the error rate, the more likely decisions are to deviate from the deterministic predictions. We did not implement an error rate for participants who use the guessing strategy but assumed that these participants are equally likely to choose both machines on each trial (i.e., pA,i,q = pB,i,q = 1/2, pDM,i,q = 0). Finally, the obtained probabilities pi,q specify the categorical distribution that generates the observed data, that is, yi,q ∼ Categorical(pA,i,q, pB,i,q, pDM,i,q).
Bayesian Implementation
We inferred the posterior distributions for each participant's model parameters, zi and ∈i (Lee and Wagenmakers 2013; Vandekerckhove et al. 2018), using the following priors. We assumed that all 17 strategies are a priori equally likely; hence, we specified a categorical prior on zi that can take values 1 to 17 to indicate which strategy participant i used for all items. For the individual error rate ∈i, we chose a Uniform(0, 0.25) prior. An error rate of zero indicates that strategies are followed faultlessly, and an error rate of 0.25 indicates that there is a 50% chance of choosing the option predicted by the strategy and a 25% chance of choosing either of the remaining two options.
Applying the model to the observed data yields, for each participant, the posterior probabilities that each of the 17 strategies was used. In addition, for each participant, we can infer how closely the assigned strategy is followed.
Simulation Study
To examine our model's ability to recover data-generating parameters, we first applied the model to generated data and compared the inferred parameters to the data-generating values (see "Results" section for the results). For each of the 17 decision strategies, we generated data for 15 synthetic participants, resulting in 255 synthetic participants. For all participants, except for those using the guessing strategy, we generated an error rate ∈i by drawing from a Uniform(0, 0.25) distribution. Each synthetic participant completed all 28 items of the Gambling-Machine Task.
Real Data Set
We then reanalyzed the Gambling-Machine Task data of 230 participants previously published by Jansen et al. (2012).Footnote 1 The data set comprises four age groups: 8–11 (n = 48), 11–12 (n = 51), 12–15 (n = 67), and 14–17 years (n = 64; see Jansen et al. 2012, for more details). After having removed 20 participants because of missing data entries (n = 9, 5, 5, 5, 1 in age groups 1, 2, 3, 4, respectively), we applied the model to 210 participants. We did not obtain Ethics Committee approval because we reanalyzed previously published data.
Model Fitting Procedure
We inferred posterior distributions for each parameter for each participant using Markov chain Monte Carlo (MCMC) sampling, which directly samples sequences of values from the posterior distribution for each model parameter (Gilks et al. 1996; Lunn et al. 2012), as implemented in JAGS (Plummer 2003) and R (R Development Core Team 2008). We ran 10 independent MCMC chains and initialized all chains with random values. For the real dataset, we collected 45,000 samples per chain and discarded the first 5000 samples as burn-in. In addition, we only used every fifth iteration to remove autocorrelation. Consequently, we obtained 80,000 representative samples per parameter (8000 per chain) per participant. In the simulation study, we collected 20,000 samples per chain and discarded the first 10,000 as burn-in. As for the real dataset, we used a thin rate of 5, resulting in a total of 20,000 representative samples per parameter per synthetic participant.
All chains showed convergence (see the online supplementary material for an assessment of the convergence and stability of our results). R and JAGS code, and the data, can be downloaded from our Open Science Framework repository (goo.gl/tkh4gE). In addition, to facilitate the use of this method by others, all steps of the modeling analysis are summarized in the online supplementary material.
Strategy Inference
We computed the mode of the posterior distribution of zi to infer, for each participant, which strategy they most likely used. In addition, to infer the certainty of the strategy assignment, we computed the proportion of zi samples that equal the mode of the posterior distribution of zi. We computed the mode of the posterior distribution of ∈i to infer each participant's error-rate parameter.
Assessment of Model Fit
To assess the descriptive adequacy of the model—that is, its ability to "fit" the observed choice data—we conducted a standard Bayesian posterior predictive check. Specifically, we generated data for each participant using the mode of the posterior distributions of their zi and ∈i parameters, and subsequently compared the generated and observed data.
Parameter Recovery
Figure 4 shows the strategy assigned to each synthetic participant in our simulation study. The synthetic participants are ordered in such a way that the data from the first 15 participants were generated with the guessing strategy, the data for the second 15 with the integrative strategy (expected value; EV), etc. We can speak of perfect recovery if the first 15 bars are all of height "guessing," the second 15 bars all of height "EV," etc. Figure 4 clearly shows this expected step-wise pattern. Specifically, 81.6% of the synthetic participants were classified correctly. Note that recovery is perfect if we use a small error rate to generate data (e.g., ∈i = .05 for all participants), clearly indicating the correctness of our implementation of the model. However, we prefer discussing a more realistic scenario with different error rates for each participant that vary between 0 and .25.
Figure S1 in the online supplementary material shows the posterior distributions of the error-rate parameter as well as the true data-generating value for 15 randomly selected synthetic participants. The mode of the posterior distribution is close to the data-generating value for some participants, indicating an adequate recovery. However, for other participants, there is a noticeable difference between the posterior mode and the data-generating value, indicating inadequate recovery. There was no systematic bias in the recovery of the individual error rates, nor a systematic relation between the bias and the standard deviation of the posterior distribution of the individual error rates (see online supplementary material; Fig. S2). Since there is no systematic bias, but a noticeable difference between the true value and the recovered value of the individual error rate for many synthetic participants, we recommend interpreting the estimated error rate at a group-level and considering individual error rates with caution.
Real Data Set: Inferred Strategy Use
The third column of Table 2 reports the percentage of the 210 real participants assigned to each of the 17 strategies according to our model. The majority of the participants used the integrative strategy, correctly integrating all three relevant cues to compute the expected value of the machines, followed by the FL > AL > CG and FL > CG > AL take-the-best strategies. In general, among the take-the-best strategies, FL seems to be a very important cue: 70.1% of the used take-the-best strategies consider FL as the first cue. It is also evident that none of the participants used the CG > AL > FL and CG > FL strategies.
Figure 5 shows the posterior inferences for strategy use, organized by the most likely strategy, for the six largest groups; the remaining 11 strategies were used by at most three participants. The header of each sub-panel contains the most likely strategy and the number of participants assigned to that strategy. The area of the circles represents the certainty of the assignment (i.e., the proportion of zi samples that equal the mode of the zi posterior): The larger the circle, the higher the certainty of the corresponding strategy assignment. It is evident that most participants were assigned with high certainty, but for some participants, related strategies are also plausible. For example, for the first participant that was assigned to the FL > AL group, the FL strategy is also very plausible.
Figure 6 shows the developmental trajectory of the six most often used strategies. With increasing age, integrative strategy use decreased, and the FL > AL > CG strategy use increased. Clear developmental changes with respect to the four remaining strategies are not evident.
Inferred error rates
The average inferred error rate was 0.08 (SD = 0.06), suggesting that, on average, participants chose the option predicted by their specific strategy on 84% of the trials and chose each of the two remaining options on 8% of the trials. Inferred error rates for individual participants varied between 0.002 and 0.23. However, as our simulation study showed that many individual error rates were not recovered accurately, these should be considered with caution.
Posterior Predictive Check
Figure 7 shows the posterior predictive check for four randomly selected participants.Footnote 2 In this figure, observed choices are represented by solid lines and generated choices by dotted lines. Filled dots indicate that the generated and observed choice coincide. The header of each subplot shows the assigned strategy and the certainty of this assignment.
To summarize the descriptive adequacy of the model across all participants, we computed for each participant the prediction error (i.e., the proportion of items for which the generated and observed choice differ). Figure 8 shows the distribution of the prediction error across all participants. The mean prediction error is 0.135, and the prediction error is below 0.20 for most participants. This suggests that, in general, the model adequately accounts for the data and that we can draw meaningful conclusions from the model's strategy indicator parameter.
Comparison of Results from the Bayesian Latent-Mixture Model and Existing Methods
The fourth, fifth, and sixth columns of Table 2 show the percentage of participants assigned to each strategy by the latent-class analysis reported by Jansen et al. (2012) and by the rule-assessment method using two different cut-off values. The two largest inferred strategy groups are the same for all three methods. However, the results obtained by the different methods differ in some crucial ways as well. First of all, we detected 15 strategy groups, whereas Jansen et al.'s (2012) latent-class analysis detected only six groups (i.e., a model with six latent classes provided the best fit to the data, according to the Bayesian Information Criterion), and the number of groups detected by the rule-assessment method depends on the cut-off value that is used. Second, the percentage of participants assigned to each group differs across the three approaches. The differences between our method and the latent-class analysis must be caused by the differences of these two modeling approaches. These differences include our use of the Bayesian rather than frequentist framework, the explicit as opposed to no explicit formalization of individual differences in error rates, and the assumption that each participant uses one out of 17 decision strategies and deviates from that strategy by an individual error rate compared to the assumption that participants with the same response pattern use the same strategy. Finally, our model outperforms the latent-class analysis on the posterior predictive check: Our model yields posterior predictions that differ from the observed data for on average 13.5% of the items, compared to 16.7% of the items for the model of Jansen et al. (2012).Footnote 3 This suggests that in addition to yielding more informative results, the Bayesian latent-mixture model is more descriptively accurate.
In this paper, we presented a Bayesian latent-mixture model approach to infer strategy use during a decision-making task. Our approach circumvents shortcomings of the traditional rule-assessment methodology (Siegler 1976; Siegler et al. 1981) and the latent-class analysis approach (Clogg 1995; Dolan et al. 2004; Heinen 1996; Huizenga et al. 2007; Jansen and van der Maas 2002; Jansen et al. 2012; McCutcheon 1987; Rindskopf 1983, 1987) by allowing for the simultaneous inference of the number and size of strategy groups, as well as the strategy that each individual participant most likely used. In addition, our approach includes individual error rates that systematically account for individual inconsistencies in following the assigned decision strategy. Finally, it does not require large sample sizes.
We illustrated our latent-mixture model approach by applying it to a data set comprising 210 children and adolescents completing the Gambling-Machine Task (Jansen et al. 2012). Our latent-mixture model combined 17 different accounts of decision making (i.e., guessing strategy, integrative strategy, and 15 different take-the-best strategies) and allowed us to infer which of these 17 strategies every participant used. We found that most participants used the integrative strategy, followed by three-dimensional take-the-best strategies that have frequency of loss (FL) and amount of loss (AL) as most salient cues. In addition, our results suggest that with increasing age, integrative strategy use decreases, but the use of the FL > AL > CG strategy increases. These findings are consistent with the results of the original analysis from Jansen et al. (2012), and seemingly different from typical findings of proportional-reasoning tasks with two attributes, such as the balance task. As discussed by Jansen et al. (2012), the decrease in integrative strategy use with age supports the fuzzy-trace theory (Reyna and Ellis 1994) which suggests a developmental increase in the dominance of gist (fuzzy) over verbatim (detailed) processing.
A major advantage of our latent-mixture model approach is that it is very flexible. The online provided code can be modified in several ways. For example, the reader can include additional decision strategies (e.g., the weighted additive model; Gigerenzer et al. 1999; Rieskamp and Otto 2006) or exclude some of the strategies. It is also straightforward to modify the prior distributions and test the impact of such modifications as a form of sensitivity analysis. Other plausible modifications are adaptations of the model to other developmental domains and tasks, for example focusing on differential strategy use when solving categorization, logical-reasoning or mathematical problems. In addition, the model could be applied in longitudinal studies to investigate developmental changes in strategy use within individual participants.
More challenging modifications and suggestions for future research involve incorporating a more theoretically motivated model of probabilistic responding given deterministic choice rules than the simple error-rate mechanism used here (Regenwetter et al. 2011). In future work, the model could also be fitted hierarchically, such that the model parameters of each participant are sampled from a group-level distribution (Farrell and Lewandowsky 2018; Lee and Wagenmakers 2013; Rouder and Lu 2005; Shiffrin et al. 2008). In a Bayesian framework, this entails that each individual-level parameter is assigned a group-level prior distribution, whose parameters (hyperparameters) are estimated as well. One advantage of a hierarchical Bayesian implementation would be that it allows for the inclusion of covariates in the model (e.g., age, gender, intelligence) such that the effects of relevant individual-difference variables on each parameter can be directly tested. In addition, it is desirable to modify our model to account for the fact that children might learn during the task; for example, just by considering the different test items, children may discover new features and therefore change their strategy (e.g., Boncoddo et al. 2010; Jansen and van der Maas 2002). This could be done by using standard Bayesian learning applied to the valence of each cue (Mistry et al. 2016). We also note that a generative assumption of our model is that each participant uses the same strategy throughout the task. This assumption is violated if strategy use depends on specific item characteristics. The method can, however, easily be extended to include such item-specific strategy use.
Finally, it should be noted that despite the advantages of the proposed mixture model and the straightforward adaptations of the code to other application areas, caution is needed when inferences are drawn. It is important to verify that the model provides a sufficient account of the data and that the results are stable, and in case of doubts, this should be made explicit. For example, participants' responses to all items are weighted equally in the model, whereas in actual datasets, it is possible that some task items are more important to distinguish strategies than others. At the same time, the reader should be aware that a latent-mixture approach will always yield a mixture of partially overlapping distributions. Therefore, although each participant is assigned to the most likely group, in some cases, another group is nearly as likely. For these reasons, a mixture analysis should always be performed and interpreted with caution (Huizenga et al. 2007).
Developmental change in strategy use is a popular topic in the developmental sciences. Inferences have been based on application of the rule-assessment methodology proposed by Siegler (Siegler 1976; Siegler et al. 1981) or latent-class analysis (Clogg 1995; Heinen 1996; McCutcheon 1987; Rindskopf 1983, 1987). Here, we proposed a model-based approach using latent-mixture models and Bayesian inference. Given the advantages of our approach—its highly informative inference and flexibility—we hope it will be applied in future studies to advance research areas covering the development of decision making, categorization, logical reasoning, and mathematical concepts.
- 1.
Jansen et al. (2012) reported one additional participant due to accidentally having included a participant with completely missing data.
- 2.
Figures for all participants are available at goo.gl/tkh4gE
- 3.
We were able to generate posterior predictions based on the inferences of Jansen et al. (2012) because the authors kindly provided us with the data and the classification of each participant.
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HS, MJ, and HMH were supported by a VICI grant of the Netherlands Organization for Scientific Research (number 453-12-005).
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Steingroever, H., Jepma, M., Lee, M.D. et al. Detecting Strategies in Developmental Psychology. Comput Brain Behav 2, 128–140 (2019). https://doi.org/10.1007/s42113-019-0024-x
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- Qualitative development
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Roger Federer has won his 18th Grand Slam title and put some extra distance on the all-time list between himself and Rafael Nadal, the man he beat , , , , in a vintage Australian Open final on Sunday. It was the year-old Federer's fifth Australian title, his first at a major since Wimbledon in , and it reversed the status quo against his nemesis, Nadal. Federer had lost six of the previous eight Grand Slam finals he'd played against Nadal, and had only previously beaten the left-handed Spaniard in 11 of their 34 matches.
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The finest tennis players in the world will have their roadmap to glory outlined on Friday, as the draw will take place for the Australian Open. As the first Grand Slam tournament of the year, the showcase Down Under is always one of the highlights of the sporting calendar, as the stars in attendance seek to make history. In the men's draw, we'll see champion Novak Djokovic try to stave off the challenge of world No. Here are all the key viewing details for the draw and a closer look at who is in contention for the title in both singles sections of the competition. Live Stream: The draw can be viewed via the tournament's official website. For Kerber, a win in the final of last year's Australian Open against Williams was the catalyst for a tremendous year.
The Scot, coming off a magnificent with a second Wimbledon crown, a successful Olympic title defence and the year-end top ranking, has lost five Melbourne finals, four of those to Djokovic. The Serb will launch his bid for a record seventh Australian Open title with a mouth-watering first round match against Fernando Verdasco. Australian Open defending men's and woman's champions Serbia's Novak Djokovic, left, and Germany's Angelique Kerber carry their trophies. Roger Federer, seeded 17th after the longest injury lay-off of his near year career, eases back in to grand slam action against qualifier Jurgen Melzer. But the Swiss master's path to an 18th grand slam title is likely to mean passing a huge third round hurdle against Japan's Nishikori.
AWS Elemental Blog
AO Classics: Rafael Nadal v Grigor Dimitrov (2017 SF)
There were some seeded casualties in the first part of the Australian Open second round, but nothing huge. On Wednesday and Thursday.
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Brand Name : star trailer
MOQ : 1 unit
Price : Negotiable
Payment Terms : L/C, T/T
Supply Ability : 300 per month
Delivery Time : 25 days
Model Number : HL-014
Size : 13000*3000*1250mm
Max payload : 80t
Certification : CCC/ISO
Type : Semi trailer
Use : Truck trailer
Material : Steel
Use:Truck Trailer Type:Semi-Trailer Material:Carbon Steel
Certification:COC ISO9001 Size:13000*3000*1250mm Max Payload:80T
Place of Origin:Shandong, China (Mainland) Brand Name:Star trailer Product name:Low Bed Trailer
Axle Brand:13TON Axle FUWA Brand Tire:11.00R20
Suspension:Steel Leaf Spring Suspension King pin:90#/50# Landing Gear:JOST
Rims:8.0 Brake System:Dual Line Braking System/ ABS
Brake Air Chamber:4 double chamber and 2 single chamber
Color:Any color will be available
Supply Ability:300 Set/Sets per Month
Packaging Details:According to customer demand
Port:Any port in China
Lead Time :
|1 - 1
|Est. Time(day)
|To be negotiated
hydraulic ramp low bed trailer are most commonly used to transport heavy vehicles (such as tractors, buses, rail vehicles, etc. ), mining and forestry machinery, road construction equipment ( such as excavators, bulldozers, loaders, pavers, cranes, etc. ) and other heavy-duty cargo.
|Trailer Model
|4 Axles 120t Low Bed Semi Trailer
|Tractor and excavator transportation
Overall Dimension
(L*W *H)(mm)
|Loading Capacity(KG)
|Axle Brand
FUWA 150x150 square beam axle, 3pcs*13 ton capacity, China
|Axle Number
|Suspension System
|Standard Mechanical suspension
|Steel Spring
|10/10/10/10 leaf spring suspension
|Main Beam
Material Q345B. Fabricated "H" beam height 500mm, Top flange thickness 18mm, Middle web thickness 10mm, Bottom flange thickness 20mm
Side beam:
20# channel steel
Tire Type
and Quantity
Double coin brand, 825R20, 12 pcs. China
|Traction Pin
|50mm or 90mm, removeable
|Spare Wheel Bracket
|2 pieces
|Tool Box
|1 Standard
|Landing Gear
JOST C200 two speed telescopic manual landing gear
Dual line pneumatic brake, SAE hose and connector
|Brake air chamber
4 units T30/30 spring brake chambers, 2 units T30 brake chambers
|Electrical System
1. Voltage: 24v
2. Receptacle: 7 ways (7 wire harness)
|Tail lamp with turn signal, brake light & reflector, side lamp etc.
|One set 6-core standard Cable.
|Side Guard
|According to customer's requirement
|Optional(yellow,red,white,blue etc.)
|Polish with wax before shipping
Our Company;
Star trailer is the 1st Chinese manufacturer that produces premium European standard semi-trailers for logistics, construction, and shipping industries.
We manufacture all kinds of standard and custom-built semi-trailers such as container chassis, low bed trailer, flatbed trailer, wind blade trailers, terminal trailers, etc
Our products have been exported to Tanzania, Nigeria, New Zealand, South Korea, Kenya, Angola, Philippines, Singapore, Malaysia, etc.
High-grade steel for semi-trailer
The steel we use is high-grade steel, it contains niobium and 0.98‰ of titanium, which keep the chassis very strong with great torsional stiffness and a low dead weight. The main beams are the strongest in the market, allowing for more load capacity. We are proud to offer every customer 5-year warranty on the mainframe.
Designed for optimial load distribution
Our trailer are designed for optimal load distribution. Instead of two web reinforcement structure design which is commonly use by other Chinese factories, we adopt the structure of width plate and stiffened plate reinforcement. As a result, our trailer has great torsional stiffness and is extremely stable when loaded.
Meet the Dream Team
Our team consists of 5 renowned senior experts, 21 engineers, and
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K.K He
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Zheng Xiaowei
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Rust Prevention Low Loader Semi Trailer With Dual Line Braking System Images


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Abstract from Monthly Return of the Department of North Carolina, Major General John G. Foster commanding, for the month of December, 1862 (headquarters New Berne, N. C.).
Present for duty.
Command. Offic Men. Aggreg Aggrega Aggregate
ers. ate te present
presen present and
t. and absent
absent. last
Eighteenth Army ..... ..... ..... 15 ......
Corps (Major
General J. G.
First Division 201 3,996 5,962 7,087 3,226
(Brigadier General
H. W. Wessells)...
Naglee's brigade... 195 3,700 4,380 5,802 .....
Heckman 96 2,236 2,847 3,759 3,860
's brigade...
Amory's brigade... 120 2,850 3,510 3,683 3,851
Lee's brigade... 108 2,802 3,526 3,879 3,908
Artillery... 58 1,400 1,732 2,230 2,175
Cavalry (Mix's)... 43 658 860 930 939
Total... 821 17,642 21,917 27,385 17,959
Organization of troops in the Department of North Carolina (Eighteen Army Corps), Major General J. G. Foster, U. S. Army, commanding, December 31, 1862.*
Brigadier General HENRY W. WESSELLS,
First Brigade.
Brigadier General LEWIS C. HUNT.
85th New York, Lieutenant Colonel A. J. Wellman.
92nd New York, Lieutenant Colonel Hiram Anderson, jr.
96th New York, Captain George W. Hinds.
85th Pennsylvania, Colonel J. B. Howell.
101st Pennsylvania, Lieutenant Colonel D. M. Armor.
103rd Pennsylvania, Lieutenant Colonel W. C. Maxwell.
Second Brigade.
Colonel THOMAS G. STEVENSON.
10th Connecticut, Lieutenant Colonel Robert Leggett.
24th Massachusetts, Lieutenant Colonel F. A. Osborn.
44th Massachusetts, Colonel F. L. Lee.
5th Rhode Island, Major George W. Tew.
Amory's Brigade.
Colonel T. J. C. AMORY.
17th Massachusetts, Lieutenant Colonel J. F. Fellows.
43rd Massachusetts, Colonel C. L. Holbrook.
45th Massachusetts, Colonel C. R. Codman.
51st Massachusetts, Colonel A. B. R. Sprague.
Lee's Brigade.
Colonel H. C. LEE.
5th Massachusetts, Colonel George H. Peirson.
25th Massachusetts, Major Josiah Pickett.
27th Massachusetts, Lieutenant Colonel Luke Lyman.
46th Massachusetts, Colonel George Bowler.
* The division and unattached brigades were organized and the commanders assigned by General Orders, Numbers 84, Headquarters Eighteenth Army Corps, December 28, 1862. The regimental commanders in First Division are given as stated in that order.


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People with an external role can't create or edit tasks.
Tasks can only be created by, edited by and allocated to internal roles. This is one of the core things that differentiates client roles and internal roles in Project.co.
You can see more information about the different roles and what they can do here: https://www.project.co/learn/kb/roles-permissions/
The reason for this is that Project.co is designed to facilitate the process of working with clients. We assume that your business is doing work for the clients business. Therefore tasks are allocated to internal people so they can do the work required to complete the task. People with external roles can see the task name and due date but they can't see any other information regarding tasks or engage with them.
This makes it clear what will be done and when for client but they don't have the ability to edit or change tasks.


text:
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The article presents information on the arrest of four suspected suicide bombers in Great Britain. Ibrahim Muktar Said, suspected of trying to bomb a bus, and Ramzi Mohammed, suspected of trying to bomb a train, were arrested at their hideout in London. In Rome, Italian police caught Hussain...
- Suspect in prostitute murder caught on CCTV. // Evening Standard;2/ 4/2014, p1
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The article reports that the 1993 Surat terror bombing suspect Mohammed Hanif Umerji Patel, who is known as Tiger Hanif, was traced in the grocery store in Bolton, England by Scotland Yard and caught from a house in Halliwell on February 16, 2010.
- Columnist's yacht bombed, maybe by terrorists. // Editor & Publisher;8/27/94, Vol. 127 Issue 35, p31
Reports that the yacht of Greek aristocrat Taki Theodoracopulos was bombed in July 1994. Damages caused by the bomb; Suspected culprit in the bombing.
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The article reports on the hunt of the 2013 Boston Marathon bombing suspects.
- Church Bombing Kills 10. Baker, Barbara G. // Christianity Today;11/13/2000, Vol. 44 Issue 13, p34
Reports on the bombing of the Sonmin Grace Church in Tajikistan on October 1, 2000. Number of casualties; Suspects in the bombing incident; Information on the church.
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Reports that the United States has bombed a chemical weapons plant in Khartoum, Sudan. Bombing suspect linked to the plant.
- Apocalypse not. Olsen, J.P. // New York;8/15/94, Vol. 27 Issue 32, p15
Reports on cases of New York bomb squad calls in which things suspected to be bombs turned out to be something else.


text:
Watercolor paper
Wonderful Life stamp set
Here is a card I am making for my son. He is getting married in October. I am going to make him a set of these for thank you notes for wedding gifts and vendors. I found out this weekend that I LOVE to watercolor! It was so much fun to stamp in Memento Black…
Lemon Zest card
This card was fun to make. It is made with watercolor paper. You stamp the citrus then spritz with water to spread the color. Did you notice the half slices? They were made buy just inking half of the stamp with your ink pad. Pretty clever, huh?


text:
This week we are going to directly address an old exam question from 2016 that popped up again this past June as part of the stage 1 assessment.
"Can Cabernet Sauvignon and Riesling be successful in the same location?"
Remember - with MW essays, the two most important things are to DEFINE YOUR TERMS and PROVIDE EXAMPLES.
So, with that in mind.... take your shot! Or at least post some ideas.
Are there places where these two varieties perform well in the same location? What does "location" mean, anyway?
Compare and contrast the preferred habitats of these two varieties. A well-rounded answer will consider a number of angles -- climate, soil, perhaps even the cultural traditions of various regions (though this is a Paper 1 question, i.e. viticulture, so probably best to keep your answers grounded).
But before I leave you to your thoughts, I wanted to make an important statement: I am an MW student, not an MW, and certainly not an adjudicator. The same applies to Sarah Bray and Sabrina Lueck. So while we are guiding this conversation, please know that we don't have all the answers. We are, effectively, studying along with you. So we are all vulnerable here! Good luck!
Kelli WhiteI found this a difficult one to structure (my feedback noted that as well). Would love to know how you or others tackled this question.
Good news, my feedback said that I had good structure and definitions. Bad news, I basically blacked out while writing furiously and can't remember much!
I remember that I argued that the varieties can be successful in the same location. And defined location as a regulated region - AVA, AOP etc.
I focused each paragraph on a similarity between the varieties. E.g relatively cold tolerant.
Can anyone give an example for a region (preferably vineyard) not in USA or Canada? I struggled here.
Did you argue they could be successful? How did you use US/Canada examples?
Mort's Block and Walton's Block from Kilikanoon in Leasingham, Clare Valley, South Australia
Really enjoying these MW threads - not studying for the MW exam, but seems like a good mix of directed study/thought for sommelier/winemaking.
Yes, I did argue that they could be successful. I defined region as appellation in my introduction, but all my examples were single vineyards.Argued that both were late budding and therefore suitable for regions with spring frosts - used Ravines in Finger Lakes, USA as an example.Argued that both were cold hardy and suitable for regions with cold winters - used Mission Hill in Okanagan, Canada as an example. Mentioned use of wind machines here too.Argued that both are heat tolerant with appropriate vineyard management - used Kiona Vineyards in Red Mountain, USA as an example here with mention of fruit shading. Also mentioned Trefethen in Napa for heat tolerance.
I remember that I mentioned the Leonetti Cellar Loess estate vineyard in Walla Walla Valley in there too but I can't remember what I used it for!
Thanks Nichole Dishman!
That's the goal Nichole Dishman and it's helpful to have your and others' insights into other properties and parts of the world!
I was gonna say clare valley as well, just because of the climate, and soil composition. also possibly from the uco and salta riegons in Argentina. Amalaya wines is making a torrontes and riesling blend.
furthermore if you want a classic example of where you can grow riesling and cabernet with great success I encourage you visit smith-madrone on spring mountain.
I was Australia eden valley - Washington yakima - South Africa cape point - I think I focused on ability to thrive on different Soils, elevations, and a preference for a long growing season for late ripening fruit, and sorta finished by talking about how they can be complimentary like riesling doing better near rivers and cabernet suffering some uneven ripening near rivers and creeks, Or potentially harvesting Riesling early for light styles and cabernet later. I had trouble defining location bc sizes of appellations vary so greatly.... I think its evident in the examiners note too that they thought Napa was too broad but were chill with the Great Southern
How about Clare Valley where Not only riesling is successful but plantings of the burner Sauvignon and many Italian varieties are added? Cannot recall the name of the winery without my notes but I was there during the presidential seminars in Australia.
I also think that defining ' successful' is crucial Which sets the tone of your argument. Does that mean that the two varieties can achieve optimal ripening? Or these two varietal wines achieve equally high quality?
Weingut Gold of Württemberg grows both Cabernet Sauvignon and Riesling. They are located near Weinstadt and one of the Cabernets that they produce is an Ortswein from Großheppach. Their website is here, but appears to be German language only.
I hinged on the definition of location, pitching micro-, meso-, and macro-climatic definitions and answering the question from each climate definition. Morrison Vineyard in Rattlesnake Hills, Eden Valley, South Africa and Pfalz all have traditions of growing the grapes side by side. I mostly argued from a meso-climatic perspective (i.e. as big as a region and as small as a single vineyard) talking about aspect and exposure as well as the mitigating influence of altitude in hilly regions.
They seemed to dig it.
Absolutely yuki saito! How would you define it?
I mentioned some of the regions discussed in this thread, with Horse Heaven Hills as a specific AVA where Cabernet Sauvignon and Riesling grow successfully (they ripen, and there are commercially successful high quality examples of each). What I also included was a region where I thought both could do well because of significant diurnal shift = Ribera del Duero, enough heat to ripen Cabernet Sauvignon and cooler micro-climates (Eastern Ribera del Duero, i.e. Soria) for Riesling. Cabernet Sauvignon is already an approved variety in Ribera del Duero, although planted in minuscule amounts.


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After the air strikes carried out by the Indian Air Force against Pakistani terror camps, torrent download search on Aditya Dhar's war-drama 'Uri: The Surgical Strike', has been suddenly increased. According to the reports, the torrent download search of 'Uri' has skyrocketed within a few hours of air strikes.
The retaliation done by the Indian Air Force has been named 'Surgical Strike 2.0'. Pulwama witnessed a dastardly terror attack, which claimed lives of more than 40 Jawans of CRPF and many got critically injured after a suicide bomber rammed a car into an army convoy on 14 February.
The Pulwama attack has been avenged, just like the Uri terror attack was avenged by the Indian Army in 2016. Vicky Kaushal starrer 'Uri: The Surgical Strike' is based on the surgical strikes on Pakistan Administered Kashmir as a retaliation for the Uri attack. The movie is written and directed by debutant Aditya Dhar and is produced by Ronnie Screwvala under his banner RVPS movies.
It seems like, high on "Josh" Indians want to relive the last surgical strike through the movie.
'Uri' is running in its seventh week and still doing a fair share of business even with competitions like 'Gully Boy'. The film has collected ₹234.71 crores gross at the Indian Box Office and has emerged as the first blockbuster of 2019.
#UriTheSurgicalStrike biz at a glance…
Week 1: ₹ 71.26 cr
Week 2: ₹ 62.77 cr
Week 3: ₹ 37.02 cr
Week 4: ₹ 29.34 cr
Week 5: ₹ 18.74 cr
Week 6: ₹ 11.58 cr
Weekend 7: ₹ 4 cr
Total: ₹ 234.71 cr
India biz.
— taran adarsh (@taran_adarsh) February 25, 2019


text:
Summerwind Resort
Navarre, FL 32566
Rates Recently Found: ($220.15 - $288.15)
3 Star
Area Attractions
Quirky Tourist Attractions in or near Florida
While in Florida, you might enjoy a visit to:
Pensacola, Florida: Wentworth Museum: Petrified Cat
T. T. Wentworth Jr. was a compulsive collector who donated all of his stuff to Pensacola -- including a mummified cat and an Abraham Lincoln head made of mulched money.
Eglin AFB, Florida: Air Force Armament Museum
Missiles, rockets, bombs (and then more bombs), and the aircraft that drop them. Bomblets, cluster bombs, bunker buster bombs, even a MOAB -- "Mother Of All Bombs."
Pensacola, Florida: National Naval Aviation Museum
A life-sized flight deck replica of aircraft carrier USS Cabot dominates one huge gallery, with vintage World War II fighter planes arrayed on the deck. The infamous "Mission Accomplished" jet of George W. Bush is here, too. 37 acres of outdoor exhibits as well.
© RoadsideAmerica.com, Doug Kirby, Ken Smith, Mike Wilkins. Information provided as an unofficial resource on attractions as a convenience to our visitors.
Navarre Hotel ChainsBest Western
Days Inn
Hampton Inn
SpringHill Suites
Cities Near NavarreCrestview
Fort Walton Beach
Gulf Breeze
Mary Esther
Pensacola Beach
Most Desired Travel Destinations:New York, NY
Chicago, IL
Orlando, FL
San Antonio, TX
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Boston, MA
Washington, DC
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text:
Опубликовано в: Работа > Танцы и развлечения в Пафос | Размещено: |
We looking for hotel DANCERS to join a dance group in Paphos and dance 1 Michael Jackson show and 1 Variety show.
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text:
"Ask the Expert" webinar series brings a much sought-after interactive, audience-driven discussion on career opportunities for legal professionals
TRU Staffing Partners, an award-winning search firm representing talent and opportunities in e-discovery and cybersecurity, and the Association of Certified E-Discovery Specialists (ACEDS), part of leading legal education provider BARBRI, today announced the companies have extended their "Ask the Experts" webinar series into 2018. The first webinar will take place on February 22 from 1:00-2:00 PM ET and is titled, "Ask the Expert: Your Questions on 'eDiscovery and…' What this Means for Your Career in 2018."
This webinar will be a discussion on how e-discovery is touching many other areas such as information governance, privacy, security, AI, the IoT, blockchain and more. The webinar will feature TRU founder and CEO Jared Coseglia along with Mary Mack, executive director of ACEDS, and Kaylee Walstad, director of strategic partnerships at ACEDS.
The companies have continued these webinars into 2018 due to high demand and record-breaking attendance. The webinars will be interactive sessions where attendees will be polled and can ask questions of the presenters to fuel important discussions facing professionals in legal technology positions.
"Now, it is more important than ever for existing and aspiring e-discovery professionals to add additional skills and certifications to their professional arsenal in order to move their careers forward," states Coseglia. "This webinar will cover a wide variety of options legal professionals have for validating and expanding their knowledge and marketability. TRU is deeply committed to helping the ESI community get these skills through our continued partnership with ACEDS, proliferation of our 'Ask the Expert' webinars, and delivery of our one-of-a-kind TRU Scholarship Program which will be a hot topic of conversation next week!"
"We are excited to continue our partnership on our 'Ask the Expert' webinar series with Jared Coseglia of TRU Staffing Partners," states Mack. "Positive feedback from attendees on our listener-driven, unscripted conversations to drive careers forward was a highlight for me last year. Expect more of our differing opinions."
TRU Staffing Partners is in its seventh year of offering the company's Scholarship Program, of which ACEDS has been a partner for all seven years. The program is designed to bring much needed training and education to the industry through partnerships with leading educational institutions. This year the program will be awarding fifty distinct scholarships including five full scholarships for the ACEDS certification package. The 2018 program is currently underway and the application can be found here.
This webinar is open to everyone; you do not have to be an ACEDS member to participate. Registration is available here.


text:
Please keep track and in good condition the costumes that were given to you for the 2020 spring play. Mrs. Misenheimer is hoping that life might change for us all, and if the school is open next year, that we might still perform our play, as it could be one of our best productions.
If you will be a high school freshman next year and you wish to still play the role you were assigned, Mrs. Misenheimer is happy to have you join us and will email you if the play will take place.


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A Wichita Beaded Hide Ball...Click the image to load the highest resolution version.
DescriptionA Wichita Beaded Hide Ball
Diameter: 2 ½ inches
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