Population Growth Model

[Avenging Eagle]

kae said:

I'm skeptical about the use of this model on student population. I'm not convinced that this model can be used for any population.

I would call the readers attention to the Critical Notes on the same page as the referenced equation.

en.wikipedia.org/wiki/Logistic_function

I'll include the text here as well:

Despite its persistent popularity, the logistic function has been heavily criticised in the field of population dynamics. One such critic is demographer, and Professor of Population, Joel E. Cohen (How Many People Can The Earth Support, 1995). Cohen explains that Verhulst attempted to fit a logistic curve based on the logistic function to 3 separate censuses of the population of the United States of America in order to predict future growth. All 3 sets of predictions failed.

In 1924, Professor Ray Pearl and Lowell J. Reed used Verhulst's model to predict an upper limit of 2 billion for the world population. This was passed in 1930. A later attempt by Pearl and an associate Sophia Gould in 1936 then estimated an upper limit of 2.6 billion. This was passed in 1955.

These criticisms are echoed by Professor Peter Turchin (Complex Population Dynamics, 2003), who nonetheless concludes that it provides a useful framework for single-species dynamics and contributes to models for multispecies interactions.

Nevertheless, the logistics curve has been a staple of models both mathematical and sociological, for instance the transformation theory of George Land, which uses the concept of the S-curve to prescribe appropriate business behaviour in various stages of a technology's growth.

Yes, the Verhulst model is popular and it's been around for a long time, but 200 years of population study appears to show that the Verhulst model can't be used for everything.

JB's model was created to try to estimate District 204's student population growth, which is a very specific goal to apply the model to. The goal is not to try and predict the population growth characteristics of Tokyo or New Delhi. As was stated in your post, the model doesn't work for everything, but I feel like it was a good choice for this specific application.

Of course, if some have their way and try to defeat the referendum, then a self-fulfilling prophecy will occur and the population numbers will decline out of misery and lost property values, and the graph will not be correct.

But since we are talking about SD 204, one of the best places to raise kids in the country, this will not be allowed to happen, and the population numbers will probably match jb's graph perfectly. Also, the precedent has already been proven, as District 203's growth has been following the same model.

[Arch]

avengingeagle said:

Of course, if some have their way and try to defeat the referendum, then a self-fulfilling prophecy will occur and the population numbers will decline out of misery and lost property values, and the graph will not be correct.

There will still be an eventual backfill.

[kae]

Well, unfortunately we can't go on feeling alone. Just because the parameters of the logistic model can be found and adjusted to fit part of the historical data, which is what was done for this example (From jb: Use D204 population data to solve for r and K simultaneously, while minimizing the sum of the forecast error.) does not mean the parameters used to generate the prediction curve are correct. All it means is that there exists logistic model parameters that allow the model to fit that part of the historical data that was used. That's all it means.

By "minimizing the sum of the forcast error", which is in essence fitting the model to the data, you must go back and analyse the r and K values to see if they make sense.

[fence]

kae said:

Well, unfortunately we can't go on feeling alone. Just because the parameters of the logistic model can be found and adjusted to fit part of the historical data, which is what was done for this example (From jb: Use D204 population data to solve for r and K simultaneously, while minimizing the sum of the forecast error.) does not mean the parameters used to generate the prediction curve are correct. All it means is that there exists logistic model parameters that allow the model to fit that part of the historical data that was used. That's all it means.

By "minimizing the sum of the forcast error", which is in essence fitting the model to the data, you must go back and analyse the r and K values to see if they make sense.

How was that data and corresponding graph someone's "feeling"? What would you suggest be used? Isn't any type of projection just that? A projection? Or are we asking for someone to guarantee events to happen in the future?

[warriorpride]

fence said:

kae said:

Well, unfortunately we can't go on feeling alone. Just because the parameters of the logistic model can be found and adjusted to fit part of the historical data, which is what was done for this example (From jb: Use D204 population data to solve for r and K simultaneously, while minimizing the sum of the forecast error.) does not mean the parameters used to generate the prediction curve are correct. All it means is that there exists logistic model parameters that allow the model to fit that part of the historical data that was used. That's all it means.

By "minimizing the sum of the forcast error", which is in essence fitting the model to the data, you must go back and analyse the r and K values to see if they make sense.

How was that data and corresponding graph someone's "feeling"? What would you suggest be used? Isn't any type of projection just that? A projection? Or are we asking for someone to guarantee events to happen in the future?

fence, I, for one, want you to guarantee me that your model will accurately predict everything for the next 20 years, or you gotta give me my money back!

Hey, and can you tell me the lottery numbers for tomorrow, too?

[fence]

No, but I do have a Magic 8 Ball. I thought of giving it to Rodman for a Christmas present.....

[rew]

This doesn't really belong here, but....I spoke to Furstenau today, he's hot on the campaign trail. I spoke with him about D204, he said NCC is committed to D204 and not rezoning anything to residential that's not on the master plan. I brought up the Kimball Homes project.

He told me we should be talking to Aurora CC which has rezoned LeHigh and large stretches of commercial property for THs and apartments.

[voteyes]

That's the most frustrating thing about the way this is district is set up. Four different cities, four different agendas, one school board. Not easy.

[refbasics]

voteyes said:

That's the most frustrating thing about the way this is district is set up. Four different cities, four different agendas, one school board. Not easy.

and 2 counties!

[refbasics]

www.suburbanchicagonews.com/napervillesun/news/756712,6_1_NA24_REDISTRICT_S1.article

D203 still crowded after enrollment decline
Fewer students doesn't always mean fewer classrooms

January 24, 2008
By Tim Waldorf Staff writer

Declining enrollment doesn't equate to freed-up space in schools, nor does it translate to fewer teachers on the pay roll, Naperville School District 203 board President Suzyn Price says.

The school board reviewed the district's enrollment projections during its Tuesday meeting. It found that enrollment has declined 5 percent since 2003, when its enrollment peaked at 18,441 students. This year, its enrollment stands at 17,584 students, down 266 students from last year.

The district is projecting that by the 2010-2011 school year enrollment will have declined 10 percent from that 2003 high, to 16,452 students.

Price calculated that this continued decline would equate to one less student per class in every grade.

"So if you talk about a decline, we're not talking about a significant decline or a lowering of classrooms," she said. "We're talking about a relatively small number, or actually a very small number, that will have almost no impact on what goes on in our classrooms, or even the make-up of our schools and our classrooms."

Superintendent Alan Leis expressed similar sentiments.

"We've got some misconceptions out there that we've got all of this empty space when, when we reviewed it before, there were really only 13 rooms that were built for classrooms that did not have a teacher and a full class in them," Leis said. "And all of them are being used by special ed or early childhood or a special reading teacher, because many of our buildings simply weren't built for those resources."

Redrawing boundaries

District 203 has explored the idea of redrawing attendance boundaries to reduce facility improvement costs.

Redistricting also remains an option for solving the overcrowding at Mill Street Elementary School, which was built for 600 students but now serves about 800.

As part of the $114.9 million facilities improvement plan it is asking voters to approve Feb. 5, the district is proposing a $7 million expansion and renovation of the school. The project adds a gymnasium and administrative area to the school and creates separate areas for buses and parents to drop off students. It also renovates the school's library, multipurpose rooms and existing gymnasium, all of which are considered too small to serve the school's large population.

Should the project not relieve Mill Street's overcrowding, the district may redraw elementary boundaries to send 200 Mill Street students who live in the Wiloway subdivision to Elmwood Elementary School.

Last year, District 203's enrollment projections indicated Elmwood could accommodate this influx if the district moved the portion of its early childhood center at Elmwood to a new $11 million proposed facility.

While the district's projected total for the entire district's 2007-2008 enrollment was only off by 42 students, its projections for Mill Street and Elmwood were complete surprises.

Mill Street's enrollment fell 49 students below the district's projections, while Elmwood's exceeded them by 31 students.

Consequently, Leis has said "we're not going to make a decision about moving attendance areas until we know for sure that they fit in Elmwood and that there's a real reason to move them out of Mill."

Contact Tim Waldorf at [e-mail] or 630-416-5270.

---------------

i posted this article for purposes of relating to D204 student population projections.

Students vs. buildings- does it eventually come down to efficiency? Same number of buildings, less students.. more cost per student- a 'better' number to show the voters?... it does not matter to me if we have a higher or lower cost per student... but what does that number encompass! .... AND why it is higher or lower?

Special Ed

.. and i won't be able to say this very well... but at a couple referendum meetings in 2006, i felt that, when 'push came to shove', that the SB & SD in 204 kind of 'blamed' special ed for having to build a new high school (??!)..i was surprised..

...from what i have seen from friends with special needs kids, and in the article above, that special ed is held in schools where there are empty classes- that sounds efficient (& it is not easy on the students to switch from school to school, and, possibly have a long bus ride) .

And, i think, the district actually 'makes money' (another terrible way to put this) on reimbursement from the state for special ed.

Where does this attitude come from?? i think, probably, spec ed parents have too much on their plates to have any impact on things; i believe there is a Spec Needs PTA but i haven't found anybody yet who is involved with it- i am sure they are too busy! which is too bad!