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In the feature vector we use Z ^ ˜ − 14 … Z ^ ˜ 14, which leads to 27 features due to omitting Z ^ 0 and Z ^ 1.

In practice, the number of initially balanced confounders could be even larger and residual confounding due to omitting all these variables from the adjustment model may become substantial, especially when these variables are strong risk factors for the outcome.

Formulating the problem more broadly than previous work, we consider the combined influence of three different sources of bias: (1) bias due to omitting a balanced covariate; (2) bias due to censoring; (3) bias due to the missing covariate being a confounder.

The funnel plots suggest that the shift to non-significance (due to omitting study #43) is likely to reflect decreased power, as the plot shows only two effect sizes below the mean effect size estimate (and six studies at or above the mean effect size estimate).

The set [ | Z ^ − n | 2 | Z ^ 1 | 2 | Z ^ − (n − 1 ) | 2 | Z ^ 1 | 2 ⋯ | Z ^ − 1 | 2 | Z ^ 1 | 2 | Z ^ 2 | 2 | Z ^ 1 | 2 ⋯ | Z ^ n | 2 | Z ^ 1 | 2 ] is invariant to shifting due to omitting the descriptor Z ^ 0 and invariant to scaling due to normalization by Z ^ 1. Furthermore it is invariant to rotation due to using the absolute value of the complex Fourier coefficients.

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Results of this study showed that safflower was significantly affected by water shortage in the soil profile due to omitted irrigation during the sensitive vegetative stage.

First, following the work of Abebaw and Haile (2013), we included several covariates in logit model specification to reduce bias, which could appear due to omitted variables.

Consequently, the selected models were severely underfitted (Additional file 1: Figure S4) which yielded error estimates with a large portion of bias due to omitted relevant variables.

Results of this 3-year study show that all vegetative and yield parameters were significantly affected by water shortage in the soil profile due to omitted irrigation during the sensitive tasselling and cob formation stages.

First, we may face an endogeneity problem due to omitted individual characteristics that may influence both the entry to the labor market (or the choice of the sector at entry) and the decision to retire at a certain point.

The possibility of estimating several channels simultaneously permits us not only to avoid some biases due to omitted variables, but also to quantify these biases by running regressions with some excluded variables on the same data.

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