重复测量设计VS时间序列分析：新西兰橙农产果年份差异技术问询

Hey there, let's work through this problem together. You've got monthly orange yield data from a New Zealand farmer spanning multiple years, folks are debating whether repeated measures design or time series is the right approach, and your core goal is to identify years with similar overall yield levels. Let's break this down clearly.

The key here is that your end target is grouping years by their overall yield level, and seasonality is both a critical feature of your data and a potential confounder. Let's address why the two approaches are being debated, and which tools will actually get you to your answer.

Why repeated measures might fall short here #

Repeated measures design is great for comparing the same subjects across different conditions—but your data is time-dependent, with inherent seasonality (predictable monthly fluctuations, like higher yields in NZ's summer months) and autocorrelation (this month's yield is correlated with last month's). Repeated measures typically assumes independent residuals, which doesn't hold for time-series data. This means any statistical tests using pure repeated measures could give misleading results because they don't account for these time-based patterns.

Time series methods solve the seasonality problem directly #

Time series techniques are built to handle exactly this kind of data. The biggest win here is seasonal decomposition, which splits your yield data into three components:

• Trend: The long-term direction (e.g., slow growth in yields year over year)
• Seasonality: The fixed, repeating monthly pattern
• Residual: Random, unexplained fluctuations

By stripping out the seasonal component, you get a "de-seasonalized" view of yield that lets you compare the true annual performance of each year—without being skewed by summer vs winter differences.

Here's a practical workflow to get you to your goal:

1. Decompose the time series to isolate annual yield trends
   Use a method like STL Decomposition (Seasonal and Trend Decomposition using Loess)—it's robust for monthly data with clear seasonality. For example, in R:

   # Assume your data has columns: year, month, yield
   library(forecast)
   # Convert to a time series object (frequency = 12 for monthly data)
   ts_yield <- ts(your_data$yield, frequency = 12, start = c(min(your_data$year), 1))
   # Run STL decomposition
   stl_output <- stl(ts_yield, s.window = "periodic")
   # Extract the trend component (de-seasonalized yield)
   de_seasonalized_yield <- stl_output$time.series[, "trend"]
   # Calculate average annual de-seasonalized yield
   annual_yield <- tapply(de_seasonalized_yield, floor(time(de_seasonalized_yield)), mean)
   

   In Python, you can use statsmodels.tsa.seasonal.seasonal_decompose to get the same result.

2. Group years by their annual yield levels
   Now that you have clean, de-seasonalized annual yield values, you have two solid options:

   • Clustering: Use K-means or hierarchical clustering to group years with similar annual yields. This is great for exploratory analysis to see natural groupings.
   • Statistical testing: Run an ANOVA on the annual yield values, followed by a post-hoc test like Tukey's HSD to identify which years have statistically indistinguishable yield levels.

3. Bonus: Combine both approaches with mixed-effects models
   If you also want to check if years with similar overall yields have the same seasonal patterns, use a mixed-effects model with a time-based autocorrelation structure. This blends the repeated measures idea (treating months as repeated observations per year) with time series logic (accounting for autocorrelation). For example, in R's lme4 package, you can add an AR(1) correlation structure to handle month-to-month dependence.

When someone argues "you should use time series", you can frame your response around your goal:

Our core task is to compare annual yield levels, and seasonality is a major confounder here. Time series decomposition lets us strip out that seasonal noise to get reliable annual yield estimates. We can then use standard statistical tools (clustering, ANOVA) to group similar years. Repeated measures alone doesn't handle the time-dependent autocorrelation in our data, but we can combine its strengths with time series logic using mixed-effects models if needed.

内容的提问来源于stack exchange，提问作者Palu