{"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 the set of real parameters, and allow constraints to be placed on the real parameter estimates.\u00a0 There is a parameter matrix for each parameter …<\/p>\n

Parameter Index Matrices (PIM)<\/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-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}]}}