<div dir="ltr"><br><div class="gmail_quote">---------- Forwarded message ----------<br>From: <b class="gmail_sendername">Caitlin Collins</b> <span dir="ltr"><<a href="mailto:caitiecollins@gmail.com">caitiecollins@gmail.com</a>></span><br>Date: Thu, Jul 30, 2015 at 3:04 PM<br>Subject: Re: [adegenet-forum] DAPC<br>To: Carly Graham <<a href="mailto:graham9c@gmail.com">graham9c@gmail.com</a>><br><br><br><div dir="ltr">Hi, <div><br></div><div>I'm glad you asked. </div><div><br></div><div>First things first, you are correct in interpreting from the xvalDapc results that you should use 100 PCs when running DAPC. (Though, I should say that you don't actually need to <i>run</i> DAPC after running xvalDapc, as the output of xvalDapc contains a dapc object that has been made by running DAPC with the optimal number of PCs as indicated by the lowest RMSE). </div><div><br></div><div>Now, I think I may know where your confusion might lie:</div><div><br></div><div>When you perform cross-validation with xvalDapc, the way it works is that DAPC gets run with varying numbers of PCs retained, <i>with some proportion of the data left out</i> (this is specified by the argument "training.set", by default 0.9). So, what "Mean Successful Assignment" is telling you is that, after xvalDapc ran DAPC with 100 PCs using only 90% of the, it was able to correctly place the left-out 10% of the data in the right group only 20.13889% of the time. The point of doing this is to identify the number of PCs that, when kept, allows us to generate a DAPC with the most informative and generalisable results.</div><div><br></div><div>By contrast, the part of the output from summary(dapc) to which I think you are referring (presumably you mean "assign.prop"?) is not actually a <i>probability</i>: it is a <i>proportion</i>. Moreover, it is the proportion of individuals that were successfully assigned to the correct group <i>when the DAPC was run with all of the data</i>. This helps to explain why it is usually much higher than the "Mean Successful Assignment" of xvalDapc, even with the same number of PCs. While cross-validation was trying to <i>predict</i> the likely group membership of unseen individuals whose data was not used to build the model, DAPC is reporting the percent successful assignment of individuals to their groups based on a model built with data from these individuals and all others in the dataset. </div><div><br></div><div>Now that this is hopefully beginning to become a little more clear, I should say (in case you have, or will, notice this and become confused) that the method used by DAPC to assign individuals to groups (leading to the assignment <i>proportion</i> reported by summary(dapc)) is a probabilistic one. Essentially, DAPC makes a probabilistic assessment based on the model. DAPC first asks: "based on the coordinate system I have generated, and given the data from this individual, where should I place this individual in multivariate space?". Then, for some individuals, it is incredibly clear that they have ended up in a corner of multivariate space that is defined and occupied by the members of a given group. For others, however, who may be placed in the space at the edge of a group or between two groups, their "most likely true group" is less clear. DAPC calculates a probability that each individual belongs in each group (storing these in the "$posterior" slot of the dapc object), and assigns individuals to the group for which their posterior probability is highest. Note that the "assign.prop" element of the output of summary(dapc) does not actually contain any information on these probabilities directly, it just tells you what proportion of the ultimate assignments were correct. </div><div><br></div><div>Taking this all into consideration, if you were actually hoping to report an "assignment <i>probability</i>", the answer is not as straightforward as choosing either "assign.prop" or "Mean Successful Assignment". "Mean Successful Assignment" might tell you more about the ability of your model to make predictions about the group memberships of individuals that are not in your sample. <i>But</i>, if your sample happened to be a perfectly <i>representative </i>sample, this would be unfair. Clearly, given all the data in the sample, DAPC was able to build a model that accurately placed individuals in the correct group 87.<span style="font-size:12.8px">01923% of the time. Furthermore, <i>this</i> is the DAPC model/output you are actually talking about (ie. the one built with all the data, not just 90% of it), so this figure is more indicative of the success of your model. Altogether, if you still wanted to make a statement about the ability of your model to make predictions about data that was not in your sample, the truth would presumably be somewhere in between those two numbers. But when talking about the DAPC outcome that you actually achieved with your dataset, the true successful assignment attained was 87.</span><span style="font-size:12.8px">01923% (just don't call it a probability!). </span></div><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">Hope that helps. </span></div><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">Cheers, </span></div><div><span style="font-size:12.8px">Caitlin. </span></div><div><br></div><div><br></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div class="h5">On Wed, Jul 29, 2015 at 10:51 PM, Carly Graham <span dir="ltr"><<a href="mailto:graham9c@gmail.com" target="_blank">graham9c@gmail.com</a>></span> wrote:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5"><div style="word-wrap:break-word">Hello,<div><br></div><div>I have been looking at the population structure of whitefish in a small lake area. I used xvalDapc to determine the optimal number of PCs to retain for the dapc analysis. When I look at the output from this xval command I see that the following:</div><div><br></div><div><div>$`Median and Confidence Interval for Random Chance`</div><div> 2.5% 50% 97.5% </div><div>0.08354526 0.12267036 0.17258877 </div><div><br></div><div>$`Mean Successful Assignment by Number of PCs of PCA`</div><div> 20 40 60 80 100 120 140 160 180 </div><div>0.1319444 0.1694444 0.1680556 0.1875000 0.2013889 0.1291667 0.1666667 0.1250000 0.1125000 </div><div><br></div><div>$`Number of PCs Achieving Highest Mean Success`</div><div>[1] "100"</div><div><br></div><div>$`Root Mean Squared Error by Number of PCs of PCA`</div><div> 20 40 60 80 100 120 140 160 180 </div><div>0.8704578 0.8361065 0.8360719 0.8177360 0.8051124 0.8730468 0.8389395 0.8772458 0.8905042 </div><div><br></div><div>$`Number of PCs Achieving Lowest MSE`</div><div>[1] "100"</div></div><div><br></div><div><br></div><div>From this I have interpreted that I should use 100 PCs. >From there when I run the dapc with 100 PCs and then look at output from summary(dapc) I have an assignment probability of 0.8701923. Where I am confused is how to interpret the “Mean Successful Assignment” from the above output. Does this also correspond to the assignment to populations? If so, is it more accurate to assume that the assignment probability is 0.2013889?</div><div><br></div><div>Thanks,</div><br><br><div>
<div style="color:rgb(0,0,0);letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;word-wrap:break-word"><div style="color:rgb(0,0,0);font-family:Helvetica;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:-webkit-auto;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;word-wrap:break-word"><div><span style="text-align:-webkit-auto">Carly Graham</span></div><div>PhD Candidate</div><div>University of Regina</div><div><br></div></div><br></div><br><br>
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