Perform Likelihood Ratio Test for Comparing Nested Single-Cell Simulation Models

Direct port and generalization of scDesign3::perform_lrt (Song et al., Nat Biotechnol 2024). Performs the likelihood ratio test to compare two nested simulation models (e.g., cell-type/covariate model vs intercept-only null model, or spline trajectory vs linear model).

Usage

calc_likelihood_ratio_test(
  alter_model,
  null_model,
  df_alter = NULL,
  df_null = NULL
)

Arguments

alter_model: Alternative model (more complex) or list of alternative models per gene, or numeric log-likelihoods.
null_model: Null model (simpler, strictly nested) or list of null models per gene, or numeric log-likelihoods.
df_alter: Degrees of freedom for alternative model (used if models are numeric log-likelihoods).
df_null: Degrees of freedom for null model (used if models are numeric log-likelihoods).

Value

A data.frame containing:

LogLik_alter: Log-likelihood under alternative model.
LogLik_null: Log-likelihood under null model.
df_alter: Degrees of freedom of alternative model.
df_null: Degrees of freedom of null model.
LR_statistic: Likelihood ratio statistic (-2 * (LL_null - LL_alter)).
delta_df: Difference in degrees of freedom (df_alter - df_null).
p_value: P-value from chi-squared test with delta_df degrees of freedom.

Examples

calc_likelihood_ratio_test(stats::rnorm(50), stats::rnorm(50))
#>    LogLik_alter LogLik_null df_alter df_null LR_statistic delta_df p_value
#> 1   0.209867384 -2.17521078       NA      NA  4.770156324       NA      NA
#> 2  -0.816187457 -0.05104740       NA      NA -1.530280112       NA      NA
#> 3  -1.909632675 -1.43635831       NA      NA -0.946548728       NA      NA
#> 4  -1.754006683  1.55479440       NA      NA -6.617602166       NA      NA
#> 5  -0.444724218  1.13885803       NA      NA -3.167164500       NA      NA
#> 6  -0.379326295  0.12214211       NA      NA -1.002936812       NA      NA
#> 7   0.642715240  2.19803557       NA      NA -3.110640656       NA      NA
#> 8   1.237260530  1.63423649       NA      NA -0.793951919       NA      NA
#> 9  -0.051097863 -0.45037410       NA      NA  0.798552473       NA      NA
#> 10 -1.948679606 -0.41957194       NA      NA -3.058215342       NA      NA
#> 11  1.519001063 -0.15984213       NA      NA  3.357686379       NA      NA
#> 12  1.429706871  1.03313603       NA      NA  0.793141681       NA      NA
#> 13 -1.124301493  0.03614347       NA      NA -2.320889921       NA      NA
#> 14  0.813475388  0.59199278       NA      NA  0.442965212       NA      NA
#> 15  0.990808956 -1.06971383       NA      NA  4.121045572       NA      NA
#> 16  1.867414806  0.62268652       NA      NA  2.489456578       NA      NA
#> 17 -0.077077193 -0.14124590       NA      NA  0.128337416       NA      NA
#> 18 -1.262153130 -0.85660697       NA      NA -0.811092312       NA      NA
#> 19  0.808672992 -1.32920339       NA      NA  4.275752756       NA      NA
#> 20  0.184479786  0.82401379       NA      NA -1.279068007       NA      NA
#> 21  2.283435625  0.25423889       NA      NA  4.058393468       NA      NA
#> 22 -0.699557505  0.03374915       NA      NA -1.466613301       NA      NA
#> 23 -0.337894425  0.13413014       NA      NA -0.944049122       NA      NA
#> 24 -1.391781848 -0.61440741       NA      NA -1.554748880       NA      NA
#> 25 -0.362493738 -0.59562430       NA      NA  0.466261130       NA      NA
#> 26 -0.136649174 -1.08912718       NA      NA  1.904956012       NA      NA
#> 27  1.680566429 -1.09314192       NA      NA  5.547416705       NA      NA
#> 28  0.232274657  0.19662648       NA      NA  0.071296354       NA      NA
#> 29  0.413836541  0.40920066       NA      NA  0.009271764       NA      NA
#> 30 -0.091474336 -2.06650036       NA      NA  3.950052050       NA      NA
#> 31  1.437691312 -0.66976918       NA      NA  4.214920990       NA      NA
#> 32  0.431343400 -1.84924878       NA      NA  4.561184359       NA      NA
#> 33  0.323456232 -1.32036864       NA      NA  3.287649748       NA      NA
#> 34  0.371082593 -0.54535115       NA      NA  1.832867494       NA      NA
#> 35  0.510086942  0.33401078       NA      NA  0.352152329       NA      NA
#> 36  1.334639648 -0.29202672       NA      NA  3.253332734       NA      NA
#> 37  0.390453588 -1.23302807       NA      NA  3.246963307       NA      NA
#> 38 -0.393405987  0.71397372       NA      NA -2.214759409       NA      NA
#> 39 -0.583498030  0.74942941       NA      NA -2.665854889       NA      NA
#> 40 -0.520313248  0.40857159       NA      NA -1.857769681       NA      NA
#> 41 -0.963829233 -3.40416260       NA      NA  4.880666737       NA      NA
#> 42 -0.231961512  0.40351882       NA      NA -1.270960660       NA      NA
#> 43  0.395099112  0.29731939       NA      NA  0.195559447       NA      NA
#> 44 -0.152276494  0.87551406       NA      NA -2.055581104       NA      NA
#> 45 -0.318809817 -0.87207427       NA      NA  1.106528910       NA      NA
#> 46  0.840816340  1.47204853       NA      NA -1.262464374       NA      NA
#> 47  1.517410542 -0.37113658       NA      NA  3.777094253       NA      NA
#> 48  1.108685625 -0.78916870       NA      NA  3.795708643       NA      NA
#> 49  0.002609576 -2.65093584       NA      NA  5.307090824       NA      NA
#> 50 -0.225667483 -1.36111468       NA      NA  2.270894392       NA      NA