{"id":193,"date":"2017-04-18T02:39:36","date_gmt":"2017-04-18T02:39:36","guid":{"rendered":"http:\/\/sites.warnercnr.colostate.edu\/gwhite\/?page_id=193"},"modified":"2017-04-18T02:39:36","modified_gmt":"2017-04-18T02:39:36","slug":"parameter-index-matrices-pim","status":"publish","type":"page","link":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/parameter-index-matrices-pim\/","title":{"rendered":"Parameter Index Matrices (PIM)"},"content":{"rendered":"

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

\n

Parameter Index Matrices (PIM)<\/b><\/span><\/p>\n

The Parameter Matrices, or Parameter Index Matrices (PIM), define the set of real parameters<\/a>, and allow constraints to be placed on the real parameter estimates.\u00a0 There is a parameter matrix for each parameter in each group, with each parameter matrix shown in its own window.\u00a0 As an example suppose that 2 groups of animals are marked.\u00a0 Then, for live recaptures, 2 Apparent Survival (Phi) matrices (Windows) would be displayed, and 2 Recapture Probability (p) matrices (Windows) would be shown.\u00a0 Likewise, for dead recovery data for 2 groups, 2 Survival S matrices and 2 reporting probability r matrices would be used, for 4 windows.\u00a0 When both live and dead recoveries are modeled, each group would have 4 parameters: S, r, p, and F (Fidelity). Thus, 8 windows would be cascaded on the screen.\u00a0<\/span><\/p>\n

The parameter matrices determine the number of parameters that will be estimated.\u00a0 Commands are available to set all the parameter matrices to a particular type, or to set the current window to a particular type.\u00a0 See Constant Matrix<\/a> for how parameters are specified constant for each occasion, Time Matrix<\/a> for a parameter matrix that is time-specific, Age Matrix<\/a> for a parameter matrix that is age-specific, Time and Age Matrix<\/a> for an example where parameters are both time and age specific, and All Different Matrix<\/a> for cases where you want every parameter value in the PIM to be different.<\/span><\/p>\n

Included on the PIM window are push buttons to Close the window (but the values are not lost — just not displayed), Help to display this help screen, PIM Chart<\/a> to graphically display the relationship among the PIM values, and +<\/a> and –<\/a> in increment or decrement, respectively, all the values in the PIM Window by 1.<\/span><\/p>\n

Although the most general method of setting up the PIM’s is via the PIM Windows, the quickest and most efficient for most models is to use the right-click and block dragging features of the PIM Chart<\/a>.<\/span><\/p>\n

Parameter matrices can be manipulated to specify various models.\u00a0 The following are the parameter matrices for live recapture data to specify a {Phi(g*t) p(g*t)} model for a data set with 5 encounter occasions and 2 groups.<\/span><\/p>\n

\u00a0 Apparent Survival Group 1<\/span><\/p>\n

\u00a0 1\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0<\/span><\/p>\n

\u00a0 Apparent Survival Group 2<\/span><\/p>\n

\u00a0 5\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 1<\/span><\/p>\n

\u00a0 9\u00a0 10\u00a0 11\u00a0 12\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 10\u00a0 11\u00a0 12\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11\u00a0 12\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 2<\/span><\/p>\n

\u00a0 13\u00a0 14\u00a0 15\u00a0 16\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0 14\u00a0 15\u00a0 16\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 15\u00a0 16\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0<\/span><\/p>\n

To reduce this model to {Phi(t) p(t)}, the following parameter matrices would work.<\/span><\/p>\n

\u00a0 Apparent Survival Group 1<\/span><\/p>\n

\u00a0 1\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0<\/span><\/p>\n

\u00a0 Apparent Survival Group 2<\/span><\/p>\n

\u00a0 1\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 2\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 1<\/span><\/p>\n

\u00a0 5\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 2<\/span><\/p>\n

\u00a0 5\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 6\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0 8\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8\u00a0<\/span><\/p>\n

In the above example, the parameters are equal across groups, i.e., the parameter estimates are forced to be the same for each group.<\/span><\/p>\n

The following parameter matrices have no time effect, but do have a group effect.\u00a0 Thus, the model is {Phi(g) p(g)}.<\/span><\/p>\n

\u00a0 Apparent Survival Group 1<\/span><\/p>\n

\u00a0 1\u00a0 1\u00a0 1\u00a0 1\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 1\u00a0 1\u00a0 1\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0 1\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0<\/span><\/p>\n

\u00a0 Apparent Survival Group 2<\/span><\/p>\n

\u00a0 2\u00a0 2\u00a0 2\u00a0 2\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 2\u00a0 2\u00a0 2\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0 2\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 1<\/span><\/p>\n

\u00a0 3\u00a0 3\u00a0 3\u00a0 3\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 3\u00a0 3\u00a0 3\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0 3\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0<\/span><\/p>\n

\u00a0 Recapture Probabilities Group 2<\/span><\/p>\n

\u00a0 4\u00a0 4\u00a0 4\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0 4\u00a0 4\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0 4\u00a0<\/span>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0<\/span><\/p>\n

Additional constraints can be placed on the real parameters<\/a> through the beta parameters<\/a> defined with the Design Matrix<\/a>.\u00a0 An example of model {Phi(g+t) p(g+t)} is shown in the Design Matrix Advance 2<\/a> section.\u00a0 The Pre-Defined Models<\/a> option provides you with a set of pre-defined models, including both PIM and Design Matrix coding.\u00a0 Thus, this option is a good way to learn how to code models in MARK.<\/span><\/p>\n

Other options for building PIMs are to Copy<\/a> the current PIM to the clipboard, and then Paste<\/a> the clipboard into another PIM.<\/span><\/p>\n

All of the examples above show upper-triangular PIMs.\u00a0 However, many data types use single rows of parameters, such as the <\/span>closed capture models<\/a><\/span>.\u00a0 <\/span>Mixture models<\/a><\/span> will use a square PIM because each mixture is a separate row.\u00a0 Even more complex PIMs are used with the <\/span>Cormack-Jolly-Seber model that has mixtures on phi<\/a><\/span>.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Index Parameter Index Matrices (PIM) The Parameter Matrices, or Parameter Index Matrices (PIM), define …<\/p>\n

Parameter Index Matrices (PIM)<\/span> Read more \u2192<\/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-193","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/193","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=193"}],"version-history":[{"count":1,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/193\/revisions"}],"predecessor-version":[{"id":194,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/193\/revisions\/194"}],"wp:attachment":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/media?parent=193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}