{"id":346,"date":"2017-05-05T19:25:18","date_gmt":"2017-05-05T19:25:18","guid":{"rendered":"http:\/\/sites.warnercnr.colostate.edu\/gwhite\/?page_id=346"},"modified":"2017-05-05T19:25:18","modified_gmt":"2017-05-05T19:25:18","slug":"median-chat","status":"publish","type":"page","link":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/median-chat\/","title":{"rendered":"Median chat"},"content":{"rendered":"

Contents<\/a> – Index<\/a><\/span><\/p>\n

\n

Median chat<\/b><\/span><\/p>\n

Estimation of the overdispersion parameter, c<\/i>, for the global model<\/a> is one of the key issues in applying Program MARK to encounter data.\u00a0 The parametric bootstrap goodness-of-fit<\/a> procedure was an attempt to develop a general procedure, but was found to be biased for Cormack-Jolly-Seber (CJS) data (White 2002)<\/a>.\u00a0 Program RELEASE<\/a> provides useful goodness-of-fit (GOF) tests and estimates of c<\/i> for the CJS data type, and programs ESTIMATE<\/a> and BROWNIE<\/a> provide similar capabilities for dead recovery data.\u00a0 However, most of the data types<\/a> in MARK do not have a useful GOF procedure to assess the validity of the global model.\u00a0 The median chat procedure is an attempt to develop a general approach to the estimation of c<\/i>.<\/span><\/p>\n

Methodology<\/b><\/span><\/p>\n

Likelihood theory leads to the deviance<\/a> and its associated degrees of freedom as a measure of the GOF of a model, with chat<\/a> estimated as deviance\/df.\u00a0 Deviance is defined as the difference between -2log Likelihood for the model of interest and the -2log Likelihood of the saturated model<\/a>.\u00a0 Asymptotically, the deviance statistic is chi-square distributed.\u00a0 However, for finite sample sizes, the deviance is not closely enough distributed as chi-square to be generally useful.\u00a0 The median chat routine is an attempt to correct for the bias of the deviance chat.<\/span><\/p>\n

The median chat approach is to simulate data with a range of c<\/i> values, obtaining a deviance chat = deviance\/df for each of the simulated data sets.\u00a0 Then, a logistic regression is performed to estimate the value of c to simulate that would result in 1\/2 of the simulated deviance\/df values greater than the observed deviance\/df, and hence 1\/2 of the simulated values less than the observed deviance\/chat.\u00a0 The procedure requires the user to specify the range of c values to simulate (lower and upper bounds, and the total number of points based on these bounds), and the number of replicate simulations to generate for each of the specified range of c values.\u00a0 Note that the lower bound can not <1, as there is no biologically reasonable model to explain underdispersed data, and there is no way to generate underdispersed data in MARK.\u00a0 Typically, a small set of c values over a wide range should be used to generate the resulting deviance\/df values, to find out the approximate range in which to simulate c to focus the simulated data around the likely value of c that will result.\u00a0 The logistic regression analysis is performed by MARK as a known fate<\/a> model.\u00a0 Output consists of the estimated value of c<\/i> and a SE that reflects the sampling variation of the estimated c<\/i>, derived from the logistic regression analysis.\u00a0 These estimates are provided in a notepad<\/a> window preceding the known fate output.\u00a0 In addition, a graph of the observed proportions along with the predicted proportions based on the logistic regression model is provided.\u00a0 The initial dialog box where the simulation parameters are specified also has a check box to request an Excel spreadsheet to contain the simulated values.\u00a0 This spreadsheet is useful for additional analysis, if desired.<\/span><\/p>\n

The two-sided 95% confidence interval on c<\/i> is obtained by picking off the 0.025 and 0.975 probability values from the logistic regression function.\u00a0 In addition, because the lower confidence bound on c is often less than1, a one-sided 95% confidence bound is also provided.\u00a0 This value is probably of more general value than the two-sided interval, given that c<\/i> has a lower bound of 1.\u00a0 Note that all of the values derived from the logistic regression function have sampling variation, which is expressed for chat as a sampling SE.\u00a0 Replicate simulation will produce slightly different results.\u00a0 Thus, the user should consider running multiple sets of simulations and taking the means of these simulations for estimates of chat and the confidence bounds.<\/span><\/p>\n

The median chat approach appears to work well.\u00a0 In comparisons for the CJS data type to the RELEASE model, the median chat is biased high, as much as 15% in one case of phi = 0.5 with 5 occasions.\u00a0 However, the median chat has a much smaller standard deviation for the sampling distribution than the chat estimated by RELEASE.\u00a0 That is, the mean squared error (MSE) for the median chat is generally about 1\/2 of the MSE for the RELEASE estimator.\u00a0 Thus, on average, the median chat is closer to truth than the RELEASE chat, even though the median chat is biased high.<\/span><\/p>\n

Available Data Types<\/b><\/span><\/p>\n

Only a hand-full of the data types in MARK can be used with the median chat procedure.\u00a0 To see which data types are possible, open the Help tab and then the Data Types menu choice.\u00a0 In the list of data types, those marked with a # sign can be run through the median chat procedure.<\/span><\/p>\n

Jolly-Seber Data Types.<\/b>\u00a0 Although none of the Jolly-Seber data types are marked with a # sign, goodness of fit of all of these data types can be assessed via the Cormack-Jolly-Seber data type.\u00a0 This is because all the lack of fit in the Jolly-Seber data types can only come from the recaptures.\u00a0 Hence, you can use the c-hat value estimated from the CJS data type for any of the Jolly-Seber data types.<\/span><\/p>\n

Huggins Closed Captures.<\/b>\u00a0 Only the <\/span>Huggins closed captures data type<\/a><\/span> can be used with the median chat.\u00a0 This is because the Huggins models condition on the number of unique animals captured, M<\/i>(t <\/i>+ 1).\u00a0 So the median chat procedures uses the observed value of\u00a0 M<\/i>(t <\/i>+ 1) to simulate data.\u00a0 However, because of this conditioning, the median chat procedure cannot be used with robust design data types and the Huggins closed capture model because the conditioning on\u00a0 M<\/i>(t <\/i>+ 1) then precludes survival rate estimation.<\/span><\/p>\n

Known Fates.<\/b> Although you can process <\/span>known fate data<\/a><\/span> with the median chat, this effort is really not assessing goodness-of-fit because you can always create a known fate model where the <\/span>deviance<\/a><\/span> is zero, i.e., the <\/span>saturated model<\/a><\/span>.\u00a0 So, what you are really doing when you run the known fate data through the median chat procedure is assessing just how much structureal lack of fit remains in your model compared to the saturated model.\u00a0\u00a0<\/span>
\n\u00a0<\/span>
\nNo individual Covariates.<\/b>\u00a0 One of the current limitations of the median chat goodness-of-fit procedure is that individual covariates<\/a> are not allowed. This is because the real parameters are passed to the simulator to generate the simulated data — a fix to avoid having to deal with the multitude of link functions<\/a> in the true model.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Index Median chat Estimation of the overdispersion parameter, c, for the global model is one of the key issues in applying Program MARK to encounter data.\u00a0 The parametric bootstrap goodness-of-fit procedure was an attempt to develop a general …<\/p>\n

Median chat<\/span> Read More »<\/a><\/p>\n","protected":false},"author":117,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-346","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/users\/117"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/comments?post=346"}],"version-history":[{"count":1,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/346\/revisions"}],"predecessor-version":[{"id":347,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/346\/revisions\/347"}],"wp:attachment":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/media?parent=346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}