Item-total correlations and alpha-if-item-removed diagnostics
Source:R/GLM_RELIABILITY.R
compute_alpha_diagnostics.RdComputes item-level reliability diagnostics for a unidimensional
scale. For each item the function returns the corrected and uncorrected
item-total correlations and Cronbach's alpha recalculated with that item
excluded. Use this alongside compute_raw_alpha to identify items that
reduce scale reliability.
Value
A data frame with one row per item and the following columns:
- item
Item name.
- alpha.if.item.removed
Cronbach's alpha computed on the remaining items after excluding this item.
- item.total.correlation
Pearson correlation between this item and the sum of all items (uncorrected).
- item.total.correlation.r.drop
Pearson correlation between this item and the sum of all other items (corrected item-total correlation, also known as r-drop). Values below 0.30 typically indicate a problematic item.
Examples
set.seed(12345)
df <- data.frame(matrix(.5, ncol = 6, nrow = 6))
correlation_martix <- as.matrix(df)
diag(correlation_martix) <- 1
df <- round(generate_correlation_matrix(correlation_martix, nrows = 1000), 0) + 5
psych::alpha(df)
#>
#> Reliability analysis
#> Call: psych::alpha(x = df)
#>
#> raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
#> 0.84 0.84 0.81 0.46 5.2 0.008 5 0.77 0.45
#>
#> 95% confidence boundaries
#> lower alpha upper
#> Feldt 0.82 0.84 0.85
#> Duhachek 0.82 0.84 0.85
#>
#> Reliability if an item is dropped:
#> raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
#> X1 0.82 0.82 0.78 0.47 4.5 0.0091 0.00059 0.48
#> X2 0.81 0.81 0.77 0.46 4.2 0.0096 0.00065 0.45
#> X3 0.81 0.80 0.77 0.45 4.1 0.0097 0.00051 0.45
#> X4 0.81 0.81 0.78 0.47 4.4 0.0093 0.00061 0.46
#> X5 0.81 0.81 0.78 0.46 4.3 0.0093 0.00072 0.47
#> X6 0.81 0.81 0.77 0.46 4.3 0.0095 0.00063 0.45
#>
#> Item statistics
#> n raw.r std.r r.cor r.drop mean sd
#> X1 1000 0.72 0.72 0.63 0.58 5 1.0
#> X2 1000 0.76 0.76 0.69 0.63 5 1.0
#> X3 1000 0.77 0.76 0.70 0.64 5 1.1
#> X4 1000 0.73 0.73 0.66 0.60 5 1.0
#> X5 1000 0.74 0.74 0.66 0.60 5 1.0
#> X6 1000 0.74 0.74 0.67 0.61 5 1.0
#>
#> Non missing response frequency for each item
#> 1 2 3 4 5 6 7 8 9 miss
#> X1 0 0.00 0.07 0.22 0.39 0.26 0.06 0.00 0 0
#> X2 0 0.01 0.05 0.23 0.37 0.26 0.06 0.00 0 0
#> X3 0 0.00 0.07 0.23 0.39 0.23 0.06 0.01 0 0
#> X4 0 0.01 0.05 0.25 0.39 0.24 0.06 0.01 0 0
#> X5 0 0.01 0.05 0.25 0.39 0.23 0.07 0.00 0 0
#> X6 0 0.01 0.06 0.24 0.40 0.23 0.05 0.01 0 0
compute_alpha_diagnostics(df = df)
#> item alpha.if.item.removed item.total.correlation item.total.correlation.r.drop
#> X1 X1 0.8172775 0.7188293 0.5813271
#> X2 X2 0.8074691 0.7577507 0.6305662
#> X3 X3 0.8050188 0.7678537 0.6423391
#> X4 X4 0.8133327 0.7328541 0.6014236
#> X5 X5 0.8129389 0.7358393 0.6034345
#> X6 X6 0.8106911 0.7430253 0.6148351