AppleTree is an application for fitting multinomial models to frequency data using the "General Processing Tree" algorithm developed by Hu and Batchelder (1994). See <http://irvin.psyc.memphis.edu/gpt/> for an introduction to "General Processing Tree" models. AppleTree can read model files and data files written for the MS-DOS "MBT" program developed by Xiangen Hu, University of Memphis, Tennessee.
AppleTree is freeware. It runs natively on both 680x0 and PowerPC Macs.
Requirements
• System 7.5 or later
• Motorola 68020 or better (no FPU required) or any PowerPC Macintosh. PowerMac recommended.
AppleTree Quick Start
You can try out AppleTree without reading the documentation first. In the AppleTree folder there are two example files to play around with.
Background
The example files are model equations and empirical data from three psychological experiments by Buchner, Erdfelder, & Vaterrodt-Plünnecke (1995).
The experiments were conducted to validate a measurement model designed to separate the contributions of recollection processes, feelings of familiarity, and guessing in a recognition memory task. The three experiments differed mainly in the way response biases were induced. In Phase 1 of the experiments, participants read words and solved anagrams. In Phase 2 participants listened to another set of words. In Phase 3, participants were shown words that were either not previously presented (distractor words) or came from either Phase 1 or Phase 2. In this phase participants had to decide from which set the words were coming from. Participants in the Inclusion Condition had to classify a word as old if they had heard, read or generated it from an anagram. Distractor words had to be classified as new. Participants in the Exclusion Condition had to classify a word as old only if they had heard it in Phase 2. All other words had to be classified as new. Participants’ responses were sampled into 16 categories. A measurement model was designed to predict the frequencies of responses in each of the categories. Please refer to the original article for a description of the categories and the model parameters. The model was fitted seperately to read and anagram words so you have two data sets per experiment to play with.
For a quick start, open the AppleTree application. Click on the "Equation File…" button in the AppleTree dialog. Select "Example Model Equations" in the AppleTree folder. Now click on the "Data File…" button. Select "Example Data" in the AppleTree folder. Now hit the "Run" button. After the fitting process has stopped, a text window appears showing the results of the fitting process for the first data set in the data file.
The AppleTree Interface
The "Model" Field
"Equation File…" Button
Click on "Equation File…" to select a file with the model equations you want to use. Equation files are ASCII text files. They must have the same format as the .eqn files used by Hu’s MBT program. The first line must contain the total number of branches in all trees. In the following lines, the equations for the branch probabilities have to be specified. There must be one line for each branch. Each line must begin with the number of the tree (beginning with 1) to which the branch belongs. After the tree number, the category number (beginning with 1) has to follow. After the category number, the equation determining the branch probability has to follow. This equation has to be a product of model parameters and/or their inverse values. See the file "Example Model Equations" for an example of an equation file.
Parameter List
The parameter list shows all parameters used in your equations file together with their current values and their status. The values shown are used as starting values for the next estimation run. You can change the value of a parameter by clicking on it. Next to the value the status of the parameter is shown. Initially all parameters are free, that is, their value is determined by the fitting process. If you click on the status field, a popup 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 variable, 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 overparametrized, 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.
"Trees" Button
Click on "Trees" to generate a graphic representation of the trees specified in the current equation file.
The "Data" Field
"Data File…" Button
Click on "Data File…" to select a file with the frequency data you want to use. Data files must have the same format as the .mdt files used by Hu’s MBT program. Each line has to begin with a category number followed by the empirical frequency for this category. You can specify more than one data set in each data file. Each data set must end with a line beginning with 3 consecutive '=' signs. See the file "Example Data" for an example of a data file.
"Data Set" Menu
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" Checkbox
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.
The "Results" Field
"To" Menu
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).
"Parameters" Check Box
If checked parameter estimates will be reported together with confidence intervals for the estimates.
"Alpha" Editable Field
This field contains the error value 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 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 tested 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 identifiablity 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 from one run to the next while G-Square values stay the same, you can be sure that your model is nonidentifiable.
"Runs" Editable Field
Here you can enter how often the estimation process is repeated to test for identifiability (see above).
The "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 likelyhood function. If it equals one, the power divergence statistic is the Pearson chi-square function.
"Stepwidth" 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 for your fitting process is different from zero, you may have to change the stepwidth to prevent the fitting process from getting stuck. You can change this parameter during the fitting process by typing '+' or '-' on your keyboard. By setting the stepwidth to zero you can get the fit for the starting values of your parameters.
"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 G-square 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.
"Iterations"
This is the number of cycles the fitting process has passed.
"G-Square"
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 selected a model file and an equation 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.
You can get AppleTree by FTP either from your local info-mac mirror, or from <ftp://cogpsy.uni-trier.de/pub>.
Version History
1.0.0
First public release
1.0.3
• For identifiability checks, all free parameters are reported in every run together with G-Square values.
• Redesign of the grafical tree generation algorithm. The former algorihm was not able to find a tree corresponding to the equations in all cases.
• Redesign of the parameter list for easier editing
• Minor cosmetic changes
References
Buchner, A., Erdfelder, E., & Vaterrodt-Plünnecke, B. (1995). Toward unbiased measurement of conscious and unconscious memory processes within the process dissociation framework. Journal of Experimental Psychology: General, 124, 137-160.
Hu, X. & Batchelder, W. H. (1994). The statistical analysis of General Processing Tree models with the EM algorithm. Psychometrica, 59, 21-47.
Read, T. R. C., & Cressie, N. A. C. (1988). Goodness-of-fit statistics for discrete multivariate data. New York: Springer Verlag.
Rothkegel, R. (1996-1997). AppleTree [Computer Program]. Trier, Germany: University of Trier.
Acknowledgements
Thanks to Axel Buchner, Edgar Erdfelder, and Martin Brand for testing and helpful comments. Thanks to Marco Piovanelli for freely distributing his excellent WASTE text engine.
