Population Growth Model

[JB]

Arch, you are too funny. Love the tagline.

[admin]

Arch, nice one.

[kae]

I was hoping some questions would get answered, but they didn't. Hmm.

[admin]

Type out the questions and hopefully JB will answer them.

[Avenging Eagle]

jb said:

admin said:

I am not. Didn't the one get a break on paying school taxes since they are not generating any kids?

Not sure. Something to look into after 3/21 though.

Seniors can get their assessments frozen for both Will and Du Page counties. Here is a link to the Du Page one.

www.dupageco.org/soa/generic.cfm?doc_id=348

They can also get their taxes deferred, but it will be earning 6% interest for the government, and must be backed up by equity in the house/condo.

Finally, they can get a 3,000 reduction in their assessment through a homestead exemption.

[kae]

The questions are above.

[admin]

You want to see the guts of the model?

[JB]

Here's the equation:



Population P, growth rate r, constant K. I've recommended you Google logistic growth for further info.

Use D204 population data to solve for r and K simultaneously, while minimizing the sum of the forecast error.

[kae]

I'm familiar with the Verhulst model equation. I know that the IPSD population data was used as it is represented by the maroon bars in the graph, but what are the Verhulst values used? What was used for r and what value was used for carrying capacity.

Doesn't the IPSD data go back earlier than 1985? If you look at the plot of the full set of data, you'll see the extended beginning. This could also extend the ending as well. I don't believe that you can forcast the date of carrying capacity using a partial data set.

The claim is that because the model fits the data, the model is correct. This is not a valid scientific proof. The data is correct because it is historical data. The model is just an equation that fits part of the data. I would find it very difficult to draw the same conclusion.

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.

[Arch]

The only observation I will make about your observation is that the 2 failures cited had the model predict below reality, not above it.

[cantretirehere]

Thanks jb, it was nice of you to post the equation for everyone. It would be even nicer if you would post the data and show us how you arrived at your results.

This fall, I asked the SB for info on their numbers and how they arrived at their conclusions estimating final enrollment. I was ignored. No response. No one answered my letter. At that point I had to assume that they did not want me to see how they arrived at their numbers and that had me wondering why. So I decided to check out the numbers on my own and come to my own conclusions. Had they just showed me their figures I could have very well become a YES vote quite easily, at that time. But we all know how that went.

jb, could you please show us your data and your calculations so that I can believe you? I would hate to think that you have something to hide. I thought you wanted to make YES voters out of NO voters. I would think that you would do everything you could to do so. By not “showing your work” as teachers would say, how can I be sure you did it right? For all you know, I could be teetering on the edge of YEShood and you could be the one to push me over. Just "show me the money".

Please don’t tell me to figure it out myself. I’m not the one holding the graph up and asking people to take it at face value. I could draw a graph like that with no data whatsoever. When I put my graphs up, I put up the data or the location of the data, and explained them fully. I’m just asking you to extend me the same courtesy.

_{The statements made in this post are strictly the opinions of the poster and not those of the administrators of said board, CFO, 204thekids, WIND204, We Care 2, the SB or any other entity. These opinions are not meant to harm, insult, or otherwise defame anyone in anyway. All deals are final. Oh wait, that last part is from a disclaimer I read somewhere else, sorry.}

[kae]

archwinsome said:

The only observation I will make about your observation is that the 2 failures cited had the model predict below reality, not above it.

I don't think the that means that two-thirds of estimates are higher.

[Arch]

kae said:

archwinsome said:

The only observation I will make about your observation is that the 2 failures cited had the model predict below reality, not above it.

I don't think the that means that two-thirds of estimates are higher.

It does suggest the hypothesis that it may underpredict. Are there ones where it grossly overpredicted like in the manner of the 2 underpredictions you cited?

[kae]

archwinsome said:

kae said:

I don't think the that means that two-thirds of estimates are higher.

It does suggest the hypothesis that it may underpredict. Are there ones where it grossly overpredicted like in the manner of the 2 underpredictions you cited?

I don't think that is a valid assumption, given the limited examples given. The only thing one could assume is that the predictions are not accurate. The logistic model is most often criticized for the assumptions it makes, which is why I wanted to see the assumptions. It is still valid for other uses.

[Arch]

That's why it was called a 'hypothesis' based on what was presented to 'counter' it.