3.2 Non-Linear Parameters - Logistic - notes

# 3.2 Non-Linear Parameters - Logistic - notes -...

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Objective [3.2] – Notes Part 3 – Logistic Be familiar with and recognize the algebraic form(s) for all three models, including their corresponding parameters and if those parameters have any meaning in the context of the functional relationship (e.g. does a parameter control the initial value, rate of change (shape), decreasing or increasing (flip), max/min, limiting values, etc.) In a linear model both parameters (linear and constant) have meaning in the “real” business world. The linear parameter is the constant rate of change of a relationship and the constant parameter is the initial value. This will NOT be that case for other models. Some parameters may not have any “real” business meaning. Some will be derived from other values that do have meaning and yet some may just be “fitting” parameters with no specific meaning. So what about the parameters in the three models we have left to study, quadratic, exponential and logistic. Do their parameters all have business meanings? How do we find their parameter values given some information (data)? What is the minimum information (data) we need to find values for all of them? Logistic Model Parameters There are two “forms” of the logistic model. Sometimes they are used interchangeably but technically one is to be used in “finite compounding “or “discrete” cases and the other in “continuous” cases. What I mean by discrete and continuous I will say later. For now it’s just ok to identify the two. You were already introduced to them before i n objective 1.8. In objective 1.11 you learned that one of the parameters controls whether the model is strictly increasing or decreasing. Before you continue you may want to go back and review those two objectives. ( ) - finite or discrete 1 ( ) - continuous 1 t kt L Dt Ab L Ae So can you recognize the parameters in each version? If not then you should review objective 1.10. They are , LA and b in the finite case and , and k in the continuous case? So unlike the linear and exponential models and like the quadratic model there are three parameters in a logistic model . So is one of them an initial value???. ....NO! Is one of them a rate???…. almost and only initially! Like the exponential model the rate is a relative rate. If you are still unclear about relative rate versus absolute rate then I suggest you go back and reread the 3.2 notes for the exponential model. So b and k are going to be identical as in the exponential, and behave the same way with this one exception. They only mean the relative rate of the logistic when th e input is “small” . That means when the logistic model is well “before” its inflection point. It’s where the logistic model “looks” exponential. In other words if a logistic and exponential model share the same initial value and values for either their b s or k s then they will be nearly identical for “small” inputs .

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3.2 Non-Linear Parameters - Logistic - notes -...

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