Scale Creation

The LaNA 2023 Linking Study achievement scales are based on Item Response Theory (IRT) scaling and population modeling, using the same psychometric models applied in TIMSS and PIRLS.

Four main analysis phases were conducted:

• Item calibration: Item parameters for new LaNA items were estimated using multiple-group IRT models; TIMSS 2019 and PIRLS 2021 item parameters for linking items were fixed (fixed item parameter calibration).
• Principal component analysis (PCA): Principal components were extracted from context data for each country to reduce dimensionality for use in population modeling.
• Latent regression population modeling: A two-dimensional latent regression model was used to generate five plausible values (PVs) per student simultaneously for mathematics and reading, estimated separately for each country using ETS MGROUP software.
• Scale transformation: Plausible values were transformed onto the TIMSS 2019 and PIRLS 2021 reporting metrics using the corresponding linear transformation constants. Results were presented as 95% confidence intervals (CIs) around average achievement estimates.

IRT calibration was conducted using the open-source MIRT package in R. The TIMSS mathematics scale was originally set to a mean of 500 and SD of 100 in TIMSS 1995; the PIRLS reading scale was established in PIRLS 2001 on the same metric.

List of Achievement Scales

• LaNA 2023 Mathematics Achievement Scale (linked to TIMSS 2019 Grade 4 mathematics scale)
• LaNA 2023 Reading Achievement Scale (linked to PIRLS 2021 reading scale)

Both scales are reported on the TIMSS/PIRLS metric (mean 500, SD 100). The LaNA Basic International Benchmarks for mathematics and reading are located at 325 scale score points (below the TIMSS/PIRLS Low International Benchmark of 400).