How to build linear or non linear models with constrained responses (sum of outputs = 1) in JMP?

[#1]

I often need to model continuous response variables that represent proportions across categories, where the responses for each sample must sum to 1 (e.g., P1=10%, P2=25%, P3=35%, P4=30%).
In Python, I use a softmax output layer to enforce the sum-to-one constraint.

• How can I build such models in JMP—either linear or neural network—while ensuring the sum of the predicted responses equals 1?
• Is there a recommended workflow (e.g., Multinomial logistic regression, neural nets with appropriate link functions)?
• Finally, can I get a Profiler that displays the predicted proportions for each category (similar to the categorical Profiler showing class probabilities)?

Thanks for any guidance or examples!

[#2]

Hi,

A very simple way to perhaps do what you're looking for is to create a nominal response column corresponding to the highest y-value and fit that to the x's using nominal logistic regression (see attached table).

Does this do what you need, and could you help me understand exactly what the use case is?  What does this data represent and what are you trying to learn from it?

[#3]

Hi Hadley,

Thanks for your help. Unfortunately, your suggestion doesn't quite address my specific need.

My Goal: I need to predict outputs with a constraint where the sum equals 1—this is common when modeling population proportions or mixture formulations based on their properties.

My Solution: I've implemented a centered log-ratio (CLR) transformation manually. The workflow is:

1. Transform outputs to centered log space
2. Fit the model on transformed variables
3. Apply the inverse transformation to ensure the constraint is respected

Here's the code for the transformation:

// Adjust zeros
epsilon = 0.0000001;
p1_adj = If(:p1 == 0, epsilon, :p1);
p2_adj = If(:p2 == 0, epsilon, :p2);
pk_adj = If(:pk == 0, epsilon, :pk);

// Scaling
sum_adj = p1_adj + p2_adj + ... + pk_adj;
p1_norm = p1_adj / sum_adj;
p2_norm = p2_adj / sum_adj;
pk_norm = pk_adj / sum_adj;

// Geometric mean
geom_mean = (p1_norm * p2_norm * ... * pk_norm)^(1/k);

// CLR transformation
y1_clr = Log(p1_norm / geom_mean);
y2_clr = Log(p2_norm / geom_mean);
yk_clr = Log(pk_norm / geom_mean);

// Inverse transformation (after prediction)
sum_exp = Exp(:y1_clr_pred) + Exp(:y2_clr_pred) + ... + Exp(:yk_clr_pred);
p1_pred = Exp(:y1_clr_pred) / sum_exp;
p2_pred = Exp(:y2_clr_pred) / sum_exp;
pk_pred = Exp(:yk_clr_pred) / sum_exp;

Additional Request: I'd also like to use the Profiler to display stacked proportions for each output—similar to how Nominal Logistic displays stacked probabilities for each label. Your solution addresses the stacking visualization, but it only predicts the probability of the highest category rather than the exact proportion of each output.

I've attached an example of the manual transformation for reference.

Best regards,