How Can the Logit Function Be Modified for a Specific Output Range?

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In summary: If not, then the domain is #[-\infty, +\infty]# (with square brackets).In summary, the conversation discusses changing the logit function, which is a sigmoid function used in neural networks and fuzzy control. The goal is to shift the graph to the right by 0.5 by replacing z with z-0.5. The function follows the pattern of z>0.5 results in f>0.5 and z<0.5 leads to f<0.5. The domain for z is [-inf, +inf], but it is noted that this may not actually include ±∞ as inputs.
  • #1
adan
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Hi,
I am looking for changing the logit f(z) = 1/(1+exp(-z)), where z range is [-inf,+inf]. I want to adapt it as follows:
if z > 0.5 then f > 0.5
z < 0.5 then f < 0.5

Thanks
 
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  • #2
Hi,
If I understand you well, you want to shift the graph to the right by 0.5. So replace ##z## by ##z-0.5##

1624359059346.png
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  • #3
BvU said:
Hi,
If I understand you well, you want to shift the graph to the right by 0.5. So replace ##z## by ##z-0.5##

View attachment 284871##\ ##
Thank you so much!
 
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  • #4
adan said:
I am looking for changing the logit f(z) = 1/(1+exp(-z))
Do you mean logistic function? That is apparently how @BvU interpreted this. I don't believe there is such a thing as a "logit" function.
 
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  • #7
Me too... :rolleyes:

Never too old to learn 😎

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  • #8
Actually, the ##f## in this thread is the sigmoid function. Vaguely remember it's used in neural networks and fuzzy control.

##\ ##
 
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  • #9
adan said:
Hi,
I am looking for changing the logit f(z) = 1/(1+exp(-z)), where z range is [-inf,+inf]. I want to adapt it as follows:
if z > 0.5 then f > 0.5
z < 0.5 then f < 0.5

Thanks
Just a technicality : Why are you using #[\-infty, \infty]#, i.e., are you considering #\pm \infty # as actual inputs?
 
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Related to How Can the Logit Function Be Modified for a Specific Output Range?

1. What is the Logit function and how is it used in adaptation?

The Logit function is a mathematical function that maps any real number between 0 and 1. In adaptation, it is commonly used to model binary response variables, such as success or failure, and to predict the probability of an event occurring based on a set of predictor variables.

2. How does the Logit function differ from other types of regression models?

The Logit function differs from other types of regression models, such as linear regression, in that it models the relationship between the predictor variables and the probability of an event occurring, rather than the relationship between the predictor variables and the outcome variable itself.

3. What are the assumptions of using the Logit function in adaptation?

The Logit function relies on the assumption that the relationship between the predictor variables and the probability of an event occurring is linear. It also assumes that the observations are independent and that there is no multicollinearity among the predictor variables.

4. How is the Logit function adapted for non-binary response variables?

The Logit function can be adapted for non-binary response variables by using a multinomial or ordinal logistic regression model. These models allow for more than two possible outcomes and use the Logit function to model the probability of each outcome occurring.

5. What are the limitations of using the Logit function in adaptation?

One limitation of using the Logit function in adaptation is that it assumes a linear relationship between the predictor variables and the probability of an event occurring. If this assumption is not met, the model may not accurately predict the probability of the event. Additionally, the Logit function may not perform well with small sample sizes or with rare events.

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