Hey Catherine, let's walk through how to figure out whether (and how much) Year affects your visit count data, using the three variables you have. First, a quick critical note: since visit counts are count data (non-negative integers), you’ll want to use generalized linear models (GLMs) like Poisson or negative binomial regression instead of standard linear regression—this accounts for the non-normal distribution of your response variable, which is essential for valid results.

1. Start with the Three-Way Interaction Model #

Your core goal is to see if Year’s effect depends on Priority and Type, so start by fitting a full three-way interaction model. This will tell you if the relationship between Year and visit counts varies across combinations of emergency/non-emergency visits and different care locations.

For R, the formula would look like:

# If Year is treated as continuous (captures linear time trend)
model_full <- glm.nb(VisitCounts ~ Year * Priority * Type, data = your_data)

# If Year is treated as categorical (tests year-to-year differences)
model_full_cat <- glm.nb(VisitCounts ~ factor(Year) * Priority * Type, data = your_data)

• Treating Year as continuous is great for detecting a steady trend over time (e.g., "each year, visit counts increase by X on average").
• Treating it as categorical lets you compare each year to a baseline (like 2007) to spot specific annual shifts.

2. Simplify the Model (If Statistically Justified) #

Next, check if the three-way interaction term is statistically significant by comparing the full model to one without the three-way interaction:

model_no_3way <- glm.nb(VisitCounts ~ Year * Priority + Year * Type + Priority * Type, data = your_data)
anova(model_full, model_no_3way, test = "Chisq")

• If the three-way interaction isn’t significant, drop it and move to the two-way interaction model.
• Repeat the process for the two-way interactions: test if Year*Priority or Year*Type are significant. If either isn’t, you can remove that term to get a more parsimonious model—just make sure you keep terms that relate to Year’s effect.

3. Quantify Year’s Impact #

Once you have your final model, here’s how to measure Year’s effect clearly:

• Continuous Year: Look at the coefficient for Year (or the slope of Year within each Priority/Type subgroup if interactions exist). For example, a coefficient of 0.05 in a Poisson model means visit counts increase by ~5% each year (since Poisson coefficients are log-transformed).
• Categorical Year: Use marginal effects (with packages like emmeans) to calculate average visit counts for each year, split by Priority and Type:

  library(emmeans)
  emmeans(model_full_cat, ~ factor(Year) | Priority * Type)
  

  This will show you exactly how visit counts change across years for each combination of emergency status and location.
• Effect Size: Check the model’s pseudo-R² (e.g., Nagelkerke’s R²) to see how much of the variation in visit counts is explained by Year (and the other variables).

4. Should You Use an Independent Model? #

An independent model (VisitCounts ~ Year) would ignore Priority and Type entirely. This is only valid if:

• Priority and Type have no effect on visit counts, AND
• There’s no interaction between Year and either Priority or Type.

In most real-world scenarios, this isn’t the case—care location and urgency almost certainly affect how often people seek care, and their relationship with time might differ. So avoid starting with an independent model; instead, use the full interaction model first and simplify only when statistical tests support it.

Final Practical Tips #

• If your data includes repeated measurements from the same individuals (panel data), use a mixed-effects model (e.g., glmer.nb) to control for individual-level variation.
• Check for overdispersion (common with count data) — if your Poisson model has a dispersion parameter much larger than 1, switch to negative binomial regression.
• Visualize your results! Plots of predicted visit counts over Year, split by Priority and Type, will make it much easier to communicate Year’s impact.

内容的提问来源于stack exchange，提问作者Catherine