Partial Correlation

partial_cor() computes partial correlations between variables while controlling for one or more other variables — the SPSS PARTIAL CORR procedure (Stata: pcorr). It answers the question "how strongly are x and y related once the influence of the control variables is removed?"

Usage

partial_cor(data, ..., controls, weights = NULL)

Arguments

data: Your survey data (a data frame or tibble). If grouped (via dplyr::group_by()), separate partial correlations are computed per group (SPSS SPLIT FILE).
...: Variables to correlate (unquoted, supports tidyselect). At least two.
controls: Control variable(s) to partial out (unquoted, supports tidyselect; SPSS BY list). At least one, must not overlap with the analysis variables.
weights: Optional survey weights (unquoted variable name), treated as frequency weights matching SPSS WEIGHT BY.

Value

An object of class "partial_cor" whose $correlations tibble holds one row per variable pair (and group combination) with:

partial_r: Partial correlation controlling for the controls
zero_order_r: The ordinary (zero-order) Pearson correlation of the pair, for comparison — SPSS /STATISTICS=CORR
df: Degrees of freedom, n - 2 - k with k control variables (non-integer for weighted data, Charter §5.1)
t_stat, p_value: t-test of the partial correlation (two-tailed, the SPSS default)
n: Listwise-complete sample size (rounded weighted N when weighted)

For three or more analysis variables, $matrices additionally holds the full partial-correlation matrix per group.

Details

Understanding the Output

Comparing partial_r against zero_order_r tells you what the controls contribute:

Partial clearly smaller than zero-order: much of the original association runs through the control variables (confounding or mediation).
Partial similar to zero-order: the association is largely independent of the controls.
Partial larger than zero-order: a suppressor situation — the controls masked part of the association.

When to Use This

Check whether a bivariate correlation survives controlling for demographics (age, education, ...)
Separate the direct association of two attitudes from what a shared cause explains

For full multivariate control with several predictors, use linear_regression instead.

Technical Details

Cases are deleted listwise across the analysis and control variables (SPSS /MISSING=LISTWISE, the PARTIAL CORR default). The partial correlation is computed from the Pearson correlation matrix of all variables via the inverse of the control-variable block; the same Pearson formula as pearson_cor is used throughout, so weighted results follow the SPSS frequency-weight convention with unrounded sum(w) in df and test statistics. Significance is two-tailed (the SPSS default).

An SPSS v29 PARTIAL CORR reference run is pending; until it lands the statistics are verified against the independent residual-of-regressions characterization (see the SPSS compatibility vignette).

Examples

library(dplyr)
data(survey_data)

# Does the satisfaction-income correlation survive controlling for age?
partial_cor(survey_data, life_satisfaction, income, controls = age)
#> Partial Correlation: life_satisfaction, income | controlling for age
#>   life_satisfaction x income: partial r = 0.448, p < 0.001 *** (zero-order r = 0.448), N = 2115
#> Use summary() for detailed output.

# Several variables, several controls
partial_cor(survey_data, trust_government, trust_media, trust_science,
            controls = c(age, political_orientation))
#> Partial Correlation: trust_government, trust_media, trust_science | controlling for age, political_orientation
#>   trust_government x trust_media: partial r = 0.019, p = 0.390  (zero-order r = 0.019), N = 1964
#>   trust_government x trust_science: partial r = 0.033, p = 0.148  (zero-order r = 0.030), N = 1964
#>   trust_media x trust_science: partial r = 0.009, p = 0.684  (zero-order r = 0.010), N = 1964
#> Use summary() for detailed output.

# Weighted (SPSS WEIGHT BY)
partial_cor(survey_data, life_satisfaction, income,
            controls = age, weights = sampling_weight)
#> Partial Correlation: life_satisfaction, income | controlling for age [Weighted]
#>   life_satisfaction x income: partial r = 0.450, p < 0.001 *** (zero-order r = 0.450), N = 2130
#> Use summary() for detailed output.

# Grouped (SPSS SPLIT FILE)
survey_data %>%
  group_by(gender) %>%
  partial_cor(life_satisfaction, income, controls = age)
#> Partial Correlation: life_satisfaction, income | controlling for age
#> [gender = Male]
#>   life_satisfaction x income: partial r = 0.455, p < 0.001 *** (zero-order r = 0.455), N = 1005
#> [gender = Female]
#>   life_satisfaction x income: partial r = 0.441, p < 0.001 *** (zero-order r = 0.442), N = 1110
#> Use summary() for detailed output.

# --- Three-layer output ---
result <- partial_cor(survey_data, life_satisfaction, income, controls = age)
result              # compact overview
#> Partial Correlation: life_satisfaction, income | controlling for age
#>   life_satisfaction x income: partial r = 0.448, p < 0.001 *** (zero-order r = 0.448), N = 2115
#> Use summary() for detailed output.
summary(result)     # full detailed output
#> 
#> Partial Correlation Results
#> ---------------------------
#> - Variables: life_satisfaction, income
#> - Controlling for: age
#> - Missing: Listwise deletion
#> 
#> Pairwise Results:
#>   -------------------------------------------------------------------------------------- 
#>   Variable 1         Variable 2  Partial r  Zero-order r    df       t      p     n  sig 
#>   -------------------------------------------------------------------------------------- 
#>   life_satisfaction      income      0.448         0.448  2112  23.037  <.001  2115  *** 
#>   -------------------------------------------------------------------------------------- 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05