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adjusting for overdispersion #40

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adjusting for overdispersion #40

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35 changes: 33 additions & 2 deletions ext_models/chen2021Fitness/model.py
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,8 @@ def fit(
k,
n,
generation_time,
reproduction_number
reproduction_number,
quasi=False
) -> Tuple[GrowthNumbers, GLMResultsWrapper]:
# adapt the data to the required format
x = t
Expand All @@ -27,6 +28,20 @@ def fit(
# The following cov matrix returned by the method is the same as invFI
cov = model.cov_params()

if quasi:
# Follow a quasilikelihood approach to adjusting for overdispersion according to
# McCullagh and Nelder, Generalized Linear Models (second edition, chapters 4.5, 9)
# Calculate the Pearson chi-square statistic
pearson_chi2 = sum((model.resid_pearson)**2)

# Calculate the dispersion factor
n_obs = model.nobs # number of observations
df_residuals = model.df_resid # residual degrees of freedom
dispersion_factor = pearson_chi2 / df_residuals

# Adjust the covariance matrix for overdispersion, but not for underdispersion (conservative)
cov = cov * max(dispersion_factor, 1.0)

# We transform these two parameters for our parameterization of interest
# and use a delta method to get the correct variance

Expand Down Expand Up @@ -65,12 +80,28 @@ def fit(
def predict(
model: GLMResultsWrapper,
t: np.ndarray,
alpha: float
alpha: float,
quasi=False
) -> ValueWithCi2:
X = sm.add_constant(t)
proba = model.predict(X)
cov = model.cov_params()

if quasi:
# Follow a quasilikelihood approach to adjusting for overdispersion according to
# McCullagh and Nelder, Generalized Linear Models (second edition, chapters 4.5, 9)

# Calculate the Pearson chi-square statistic
pearson_chi2 = sum((model.resid_pearson)**2)

# Calculate the dispersion factor
n_obs = model.nobs # number of observations
df_residuals = model.df_resid # residual degrees of freedom
dispersion_factor = pearson_chi2 / df_residuals

# Adjust the covariance matrix for overdispersion, but not for underdispersion (conservative)
cov = cov * max(dispersion_factor, 1.0)

# we need to estimate confidence interval for predicted probabilities using the delta method as well

# the proportion is a function of the parameters
Expand Down