The AppleTree Interface

Menus

"Model" Menu

"Enter Model File..." Menu Item
Click on "Enter Model File..." to select a file with the model you want to use. The file format for Model files is specified in the File Formats Page.
"Enter Model from Window" Menu Item
This command enters the model specified in the topmost window into AppleTree. The topmost window can be a text document or a tree graph document.
"New Model in Graph Editor" Menu Item
This command lets you build tree models graphically. It opens an empty tree graph window with three pop up menus on the top. To build a new model first select "New Tree..." from the "Trees" menu. Enter a name for the tree. The tree name appears in the window together with a circle symbolizing the root node. The circle is hilited indicating that it is currently selected. You can select nodes by clicking on them. Next, select "New Category" from the "Categories" menu. Enter a name for the category. As soon as a category is specified bifurcations can be added to the tree by selecting an existing parameter or a new parameter from the "Parameters" pop up menu.
"Edit Model in Graph Editor..." Menu Item
This command lets you edit an existing model file graphically. To edit a model select a model file from the file select box. Select the node you want to edit and use the pop up menus on the top of the graph window to edit the node.

"Data" Menu

"Enter Data File..." Menu Item
Click on "Enter Data File..." to select a file with the frequency data you want to use.  The file format for Data files is specified in the File Formats Page.
"Generate Expected Data Set" Menu Item
This command can be used to generate "ideal" data for a given model. It computes expected frequencies from the parameter values specified in the parameter list in the "Model" field. The frequencies for the trees are taken from the currently active data set. If no active data file is specified (that is, the "Data" field in the "AppleTree" window is empty) frequencies for the trees are set to 100. Therefore, in this case category frequencies indicate the expected percentage of events in a tree falling into a certain category.

AppleTree Main Window

"Model" Field

This field contains information about the model that is currently in use. You can enter a new model by using the model menu. You can also drag model files from the Finder and drop them onto the model field or double click it in the finder if the file name ends with ".eqn".
"Parameters" List
The "Parameters" list shows every parameter used in your model file together with its current value and status. The values shown are used as starting values for the next estimation run. They can be edited by clicking on them. Next to the value the status of the parameter is shown. Initially all parameters are free, that is, their values are determined by the fitting process. If you click on the little arrow button to the left of the status information, a pop up menu appears, allowing you to change the status of this parameter. By selecting "fixed", the parameter is treated as a constant. By selecting the name of another parameter, you can set this parameter equal to the other parameter.
"Degrees of Freedom"
These are the degrees of freedom for the model given the set of current restrictions. The degrees of freedom are determined by
(number of categories)-(number of free parameters)-(number of trees).
If the result is a negative number, your model is over parametrized, that is, it does not contain enough restrictions to determine a unique value for each parameter. If the result equals zero, the model contains enough restrictions to determine a unique value for each parameter (if it is identifiable) but it is not possible to test the fit of the model statistically.

"Data" Field

This field contains information about the data file that is currently in use. You can enter a new data file by using the model menu. You can also drag data files from the Finder and drop them onto the data field.
"Data Set" Pop up Button
The "Data Set" menu shows the data sets specified in the current model file. Use this menu to select the data set to which you want to fit the current model.
"Batch Mode" Check box
If "Batch Mode" is checked, the fitting process will start with the current selection of the "Data Set" menu and proceed down the data set list until the last data set is reached.

"Results" Field

"To" Pop up Button
The "To" menu lets you select where the results of the fitting procedure will be reported to. If you select "Nowhere" no results will be reported, except the ones visible in the parameter list and the "Fitting" field (see below).
"Power" Check Box
If checked a post-hoc power analysis for the Power Divergence statistic is computed. The power analysis code was originally written by Franz Faul (University of Kiel) for G*Power (Erdfelder, Faul, & Buchner, 1986). In the "Alpha" editable field the Error 1 probability for the power analysis can be entered. By checking the "w" check box you can specify the critical effect size (Cohen's w) in the corresponding editable field. Leaving "w" unchecked provides a means for determining the power of hierarchical model tests developed by Edgar Erdfelder, University of Bonn. Suppose you have two models A and B, where B is a more restrictive version of A. You can compute the power of a test of model B given that model A is true by using the expected category frequencies for model A (as provided by the "Generate Expected Data Set" command, see above) as empirical frequencies for model B. The critical effect size for a test of model B as a function of the difference between the parameter vectors for models A and B can be shown to be
w=sqrt(PD-Fit/N),
where PD-Fit is the value of the Power Divergence statistic and N is the total frequency of all categories in all trees. See forthcoming publications by Edgar Erdfelder for details.
"Parameters" Check Box
If checked parameter estimates will be reported together with confidence intervals for the estimates. The "Alpha" editable field contains the error probability for which confidence intervals are computed.
"Frequencies" Check Box
If checked, empirical and predicted frequencies are reported, together with the ratios of these frequencies.
"Fisher Information" Check Box
If checked, the inverse of the observed Fisher information matrix is reported. This is an estimate of the variance/covariance matrix of the free parameters.
"Identifiability" Check Box
If checked, the model will be checked for identifiability. A model is identifiable if the estimation process always comes to the same result for a given model and a given data set. AppleTree provides a simple check for identifiability by repeating the fitting process with different (randomly determined) starting values for the parameters. For each run, all free parameters together with the G-Square values are reported. After the last line, ranges for all free parameters and ranges for G-Square values are reported. If parameter estimates differ substantially between two runs while G-Square values stay the same, you can be sure that your model is non identifiable (given that the global minimum was found). In the "Runs" editable field you can enter how often the estimation process is repeated in the identifiability check (see above).

"Fitting" Field

"Lambda" Editable Field
This is a parameter used for determining the fit of the model. The fit is determined with the family of Power Divergence statistics proposed by Read & Cressie (1988). If lambda equals zero, the power divergence statistic is the likelihood ratio G-Square. If it equals one, the power divergence statistic is the Pearson Chi-Square function. The lambda parameter also affects the fitting process, that is, the fitting process minimizes the Power Divergence statistic for the specific lambda value chosen.
"Stop-Delta" Editable Field
This parameter controls when the fitting process stops. If the absolute difference between the parameter values in run n and the corresponding parameter values in run n-1 is smaller than stop-delta and the absolute difference between the Power Divergence statistic in run n and in run n-1 is also smaller than stop-delta, then the fitting process stops and the results are reported.
"Step Width" Editable Field
With this parameter, you can control the amount of change for the parameters in every iteration of the fitting process. If the lambda value for your fitting process is different from zero, you may have to change the step width to prevent the fitting process from getting stuck. You can change this parameter during the fitting process by clicking on the little arrows to the left of the editable field or by typing '+' or '-' on your keyboard. By setting the step width to zero you can get the fit for the starting values of your parameters.
"Iterations"
This is the number of cycles the fitting process has passed.
"PD-Fit"
This is the value of the Power Divergence statistic (see above).

"Run" Button

Hit this button to start the fitting process. This button is disabled until you have entered a model file and a data file. When the fitting process is running, the button text changes to "Cancel" and you can stop the fitting process by hitting the button again. You can also stop the fitting process with the return key or by typing command-period.

The Graph Editor Window

Graph Editor Windows are used for displaying and editing models graphically. Categories are indicated by blue rectangles. Links are indicated by green lines. Nodes are displayed as black circles. If you click with the mouse on a node, the node becomes hilited indicating the selected state. Selected nodes can be altered by the pop up buttons on top of the window. Clicking anywhere in a tree graph window and moving the cursor lets you drag the tree picture into any other window supporting Drag and Drop for PICTs.

"Trees" Pop up Button

This menu lets you create and delete trees. "New Tree..." puts a new tree at the bottom of the graph editor window. "Delete Tree" deletes the currently selected tree.

"Parameters" Pop up Button

This menu lets you select a parameter for the bifurcation starting at the selected node.

"Categories" Pop up Button

This menu lets you choose a response category the selected node ends in. You can also use this menu to "cut" a tree at a given node. If you select a node anywhere in a tree and choose a category for this node, any links starting from this node will be cut.
 
 

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