R语言中fa()与factanal()函数的差异解析咨询

Hey there! Let’s break down why fa() (from the psych package) and factanal() (base R’s built-in function) are giving you different results for your exploratory factor analysis (EFA) — it all boils down to their core purposes and default settings.

1. Core Purpose: Exploratory vs. Confirmatory #

• factanal(): This tool was built primarily for confirmatory factor analysis (CFA), not EFA. It’s meant to test a predefined factor structure (e.g., “I suspect these 6 variables map to Factor A, and 5 to Factor B”). Even if you use it for EFA by specifying a number of factors, it still operates with that confirmatory mindset, using strict maximum likelihood (ML) estimation to fit your data to a fixed model.
• fa(): This is a purpose-built EFA tool from the psych package. Its entire design is focused on uncovering hidden factors without you having to guess the structure upfront. It supports multiple estimation methods tailored for exploration, making it the go-to choice for your work with 23 variables and 1777 observations.

2. Default Estimation Methods #

• factanal(): Defaults to maximum likelihood (ML). ML requires your data to follow a multivariate normal distribution, and it optimizes the fit between your observed covariance matrix and the one implied by the factor model. While ML works for CFA, it’s not always the best fit for EFA, especially if your data doesn’t meet normality assumptions.
• fa(): Defaults to principal axis factoring (PAF). PAF focuses on extracting shared (communal) variance from your variables, ignoring unique variance initially. It’s far more robust to non-normal data — a huge plus when you’re still exploring your dataset’s underlying patterns. You can switch to ML with fm = "ml" if you want, but PAF is the standard for EFA.

3. Rotation (Critical for Interpretability) #

• factanal(): Defaults to no rotation. Without rotation, your factor loadings will often be messy — variables might load weakly on multiple factors, making it impossible to assign clear, meaningful labels to each factor. You have to explicitly set rotation = "varimax" (or another rotation method) to get interpretable results.
• fa(): Defaults to varimax rotation, an orthogonal rotation that maximizes the variance of factor loadings. This is a standard step in EFA because it cleans up the loading matrix, making it easy to see which variables cluster together under each factor. No extra work needed here — it’s built to give you interpretable results out of the box.

4. How They Handle Unique Variance #

• factanal(): As part of its ML fitting, it estimates unique variance (the variance in each variable that isn’t explained by the factors) directly. This can shift results compared to PAF, which treats unique variance as residual and focuses first on communal variance.
• fa(): With PAF, it starts by estimating communalities (how much variance each variable shares with others) and iteratively refines them. This aligns perfectly with EFA’s goal of finding underlying common factors that drive your variables.

5. Output Focus #

• factanal(): Prioritizes model fit statistics (like chi-square, RMSEA, CFI) because it’s built for testing predefined models. It gives factor loadings, but the output is structured around whether your model fits the data, not around exploring new factors.
• fa(): Prioritizes interpretability and exploration. It gives you clean loading matrices, communalities, factor scores, and even diagnostic tools like scree plots to help you decide how many factors to keep. The output is designed to guide you through uncovering the hidden structure in your data.

If you want to see how the two functions stack up with identical settings, try:

• For fa(), use fa(data, nfactors = X, fm = "ml", rotate = "none") to match factanal()’s defaults.
• For factanal(), use factanal(data, factors = X, rotation = "varimax") to match fa()’s default rotation.

But remember: For your exploratory work, fa() is the right tool. It’s built specifically for uncovering factors without prior assumptions, which is exactly what you need with your 23 survey variables. factanal() shines when you have a specific factor structure you want to test.

内容的提问来源于stack exchange，提问作者Mehdi Tarik