model help

[DBurke]

I would appreciate help with this model labeled 10-20 that I've attached to this post. It is a model that we have developed to examine the critical factors in recruiting and retaining teachers. We’re having a problem that we have not been able to resolve with several simultaneous equations that are being generated. The basic model is a co-flow of an aging chain of teachers moving through their salary ladder with a parallel chain of arbitrary effectiveness units associated with each step in the aging chain. It is actually a double co-flow because we treat teachers entering from pre-service majors separately from teachers entering through a career change. We have built in a series of variables based on the education literature that influence recruiting, retention and effectiveness. For example, we have an experience variable increasing effectiveness that kicks at the third year and we have a professional development variable that can increase effectiveness in any year depending on how good the professional development is and how many teachers are involved. The most interesting variables impact both retention and effectiveness. So, for instance, in the first two years a induction/mentoring variable both increases retention and increases effectiveness. A second multifaceted variable, working environment, is where we are running into problems. We do two things with this variable. We use it along with relative compensation to determine a variable, job satisfaction. Job satisfaction influences teacher leaving rates. We have four separate job satisfaction variables because at different times in their career compensation and working conditions have different values to the teachers. Working conditions also impact effectiveness, and it is that our problem lies. An increase in working conditions produces an increase in a working-condition multiplier that, in turn, increases the adjusted effectiveness leading to an increase in average effectiveness. This then increases the value of student needs and student attendance, two factors in working conditions. You can see this is a loop then that generates a simultaneous equation, actually two simultaneous equations. We have tried all sorts of variations of Active Initial but have not been able to open the loop so I would really appreciate it if anyone can tell me what I’m doing wrong or can come up with a way of opening this loop.

I know that our model is kind of clunky, so if you see any ways to simplify it, that would be great. We do need to treat the teachers as an aging chain rather than as a single pool because of the salary step schedule and other differences such as attrition rates that are related to their length of service.

[LAUJJL]

Hi

The fist way to simplify your model is to use subscripts.
It looks awfully complicated without it.
A second reflexion is why you feel necessary to use 25 stages through a 25 years carreer?
Why not simplify your model and take only 5 or 4 stages?
A third way to simplify your model is to take away at least for
some time, several parameters and to add them if necessary
later on.
It is always better to start with a simple model to get some understanding first before jumping into eventual unnecessary details!
I presume you did not do it, otherwise you would have already solved the instantaneous equation in a previous state of development.
Regards.
JJ

[Edited on 9-12-2006 by LAUJJL]

[LAUJJL]

Hi

About the simultaneous error there are several ways to solve the problem.
You must first study the chain of causal loops, and determine if effectively variable1 influences variable2 that influences variable 3 etc... that influences back variable 1 IN THE SAME TIME STEP. If it is the case, then it is normal that Vensim reports an error, because the loop will loop endlessly as it is written. The solution is to tell Vensim how to stop the looping
by setting a simultaneous equation or by a find zero function
(look at the documentation).
A second way is to add a level in the loop. By example, one can consider that a variable influences another variable but only the next time step. One has to put the variable into a level that will keep its value for the next step and will influence the variable in question.
Regards.
JJ

[LAUJJL]

Hi

I have modified my first post, because I used time steps instead of stages.
Another reflexion about your model, is : did you test your model against past data? Briefly, is your model a product of your imagination, experience without having been tested with past data, or does its results stand too the comparison with the past.
In the first case, you are left with your dreams, in the second case, dreams will be limited and the model may be more useful too.
From my past experiences, trying to build models, with no reference to the past, has been the main error and has always delivered unuseful models.
Regards.
JJ.

[bob@vensim.com]

The simultaneous loops you identify are not initial simultaneities - but active. The first one occurs because, in a nutshell, effectivness depends on attendance and attendance depends on effectiveness. The correct way to do this would be to have attendance depend on perceived effectivness, where this perception is a smooth of effectiveness. Simply changing the equation for "Ave Effectivness"

Ave Effectiveness= SMOOTHI(("1-3 Adjusted Effectiveness"+"4-11 Adjusted Effectiveness"+"12-24 Adjusted Effectiveness"
+"25 Adjusted Effectiveness")/Year End Teachers,TIME TO PERCEIVE EFFECTIVNESS,INITIAL AVERAGE EFFECTIVNESS)

will fix this. TIME TO PERCEIVE EFFECTIVNESS shold be 1-3 years. INITIAL AVERAGE EFFECTIVNESS should be set to reflect starting conditions.

I hope that is helpful - I tend to agree with JJs comments.

[Dan Burke]

JJ and Bob,

Please excuse the inexcusable tardiness of my reply thanking you for your help with my model. Apparantly my consience has a long delay that I need to take into account. I wanted you to know that I took a lot of your advice about simplifying the model and used Bob's suggestion on dealing with the simulataneous equation. It worked but then I was able to reformulate the model and get rid of the simultaneous equation altogether.

In response to some of your comments:
1. I should have used subscripts.
2. The basic model does reproduce past performance of the system. We set it up using actual teacher pool sizes and leave rates that been seen for over 15 years, so while the pool numbers over time are not exactly matched to real world data they are pretty close and match the trends well.
3. All the variables we used to modify leave/stay decisions and effecitiveness are those that the research literature has shown to make an important contribion to teachers' stay/leave decisions and to their effectiveness. The functions defining the value for each variable that we used to modify teacher leave rates or effectiveness either come out of a detailed study of the research literature, of research we have done, or from extensive discussion with education practioners. In cases where this is not so, the value range of the variable is sensible and we specify that the shape of the function needs further research to determine. This still allows the districts to run "what-if' experiments that are useful.
4. We used a separate level for each year of service because of the disparate leaving behavior and responce to the variables that influence their behavior and effectiveness. Averaging in a few boxes would have lost a lot of information of value to school districts in trying to allocate resources between rectruiting and retention programs and between programs aimed at increasing teacher effectiveness.

Again I apologize for this late reply and thanks to both of you for your invaluable help