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The Wald test estimates the test statistic by computing the unrestricted regression equation, without imposing any coefficient restrictions, as specified by the null hypothesis.
where σ ̂ 2 = 1 n ( T - 1 ) S 1 ( γ ̂ 1 ), S0 are the residual sum of squares from the restricted regression, S 1 ( γ ̂ 1 ) are the residual sum of squares from the unrestricted regression, and γ 1 ̂ is the threshold parameter that minimizes the residual sum of squares.
The single threshold procedure requires comparing the residual sum of squares from the restricted regression, Equation (2), to the unrestricted regression which allows for a single threshold: u t = u i, t ∗ + β 0 ( y i, t - y i, t ∗ ) I ( q i, t ≤ γ ) + β 1 ( y i, t - y i, t ∗ ) I ( q it > γ ) + e it (5).
Diagnostic parameters (unrestricted regression): Number of observations = 738.
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41 Mixed effects univariate meta-regression (unrestricted maximum likelihood) was used to allow for residual heterogeneity and to explore the observational effect of continuous covariates on effect size.
In this paper, the ARDL approach to co-integration is estimated using the following unrestricted error correction (UREC) regressions.
Meta-regression analyses using unrestricted maximum likelihood model were performed to assess the factors explaining the heterogeneity of risk ratios across studies.
We initially pooled all azole interventions versus all amphotericin B trials for response and conducted a multivariable meta-regression using the unrestricted maximum likelihood method assessing the impact of individual azoles on the overall estimate of effect and the individual delivery methods of amphotericin B on overall estimate[ 12].
Park [10] used different VAR models to analyze the prices of fodder and cows, drawing conclusions that Bayesian vector auto-regression (BVAR) model and unrestricted vector VAR (UVAR) model generated forecasts which were superior to both a restrict VAR (RVAR) model and a vector auto-regressive moving average (VARMA) model in this case.
Log likelihood ratio test of the base case model was compared to the sum of the log likelihood ratio test for the unrestricted model (i.e. random-effects logit regression of sample EQ5D < 0.69 and random-effects logit regression of sample EQ5D ≥ 0.69).
Regarding the parent scales, the model with assumed non-statistically significant regression weights also exhibited a slightly significant difference from the unrestricted baseline model.
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