如何基于拟合得到的Gompertz方程参数计算中点值？

First, let's recap the work you've already completed: you've fitted a Gompertz growth model using the grofit package in R, and extracted the key parameters:

• μ (growth rate) = 36.162016
• λ (lag phase) = 7.9800164
• A (asymptotic value) = 100

The Gompertz equation you're using is:

y = A * exp(-exp( (μ * e * (λ - time)) / μ + 1 ))

Where time ranges from 1 to 12, each representing the midpoint of a 15-day cycle.

Step 1: Optional - Extract Parameters Directly from the Model #

Instead of manually typing the parameters, you can pull them directly from your fitted mdl object to avoid human error:

# Extract coefficients from the fitted model
gompertz_params <- coef(mdl$gcFit)

mu <- gompertz_params["mu"]
lambda <- gompertz_params["lambda"]
A <- gompertz_params["A"]

Step 2: Calculate Midpoint Values #

Use the Gompertz equation to compute the predicted midpoint values for each time point. Here's the full R code:

# Define your time vector (midpoints of 15-day cycles)
time <- 1:12

# Calculate predicted values using the Gompertz equation
y_midpoints <- A * exp(-exp( (mu * exp(1) * (lambda - time)) / mu + 1 ))

# Combine time and midpoint values for easy viewing
results <- cbind(Time_Cycle_Midpoint = time, Predicted_Midpoint_Value = y_midpoints)

# Print the results
print(results)

What this does: #

• exp(1) calls the natural constant e required for the equation
• The cbind() function organizes the time points and their corresponding predicted values into a clean table
• Running print(results) will show you the midpoint value for each of the 12 15-day cycles

内容的提问来源于stack exchange，提问作者89_Simple