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We calculated the LEO.NB.SingleMarker (LEO) score, which is a relative fitting index that compares the model fitting p-value of the causal model for a gene x i causing ME to that of the next best competing model.
However, while the model SNP → Methylation → Expression fits the data well (model fitting p-value p = 0.10), the model SNP → Expression → Methylation does fits the data poorly (model fitting p-value p=6.4e-5).
This model fitting p-value is calculated using the model chi-square statistic statistic.
For each causal model a chi-square test based model fitting p-value was calculated with the structural equation modelling (SEM) R package [ 46].
Of these, 20 combinations have a strikingly high LEO score of 3 or higher; for most of these 20 combinations, the model fitting p-value of the causal model SNP → Methylation → Expression is above 0.01, indicating a good fit and lending further credence to these results (Additional file 4: Table S3).
The relative fit of causal model 1 (SNP→Methylation→Expression) was assessed using the single anchor local edge orienting score (LEO.SingleMarker), which is the logarithm (base 10) of the ratio of the model fitting p-value divided by that of the next best fitting alternative model [ 19].
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The model fitting p-values of these combinations are generally worse (below 0.01), indicating that the linear structural equations models do not fit the data as well and suggesting caution in interpreting the results.
A likelihood ratio test tells us that adding this variable provides a statistically significant improvement in model fit (p-value of 0.0052).
Adding in covariables that were not significant in the univariate analysis (USA or non-USA-based trial; NYHA class; ischaemic aetiology) did not significantly improve the model fit (p values: 0.21 0.71), and they were therefore discarded.
Potential confounding variables were considered for inclusion in the models based on a priori criteria: significance in previous work, significant contribution to the model fit (P value of the Wald χ <0.05), or confounding the association between the main variable of interest and the outcome by more than 10%.
We selected the most parsimonious model among the models with a goodness-of-fit p-value >0.05, and with the lowest AIC and DIC values.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com