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A message declaring that in this sample no risk sets with three or fewer controls exist. Otherwise, a table illustrating risk sets with such few controls is displayed. This is a warning for the loss of efficiency of the design that may occur when the subcohort becomes small due to many failures or censorings.

A new stset definition that fixes the entry and exit time to the present t, t0 and d variables. This is necessary because nonsubcohort cases cannot rely on the original entry times. Note that after stcascoh, the total analysis time is reduced to Data must be prepared for case—cohort analysis by stcascoh before using this command.

Description stselpre returns estimates and standard errors from proportional hazards fit to case—cohort data. Coefficients are estimated according to two methods: 1 the Self—Prentice method where risk sets use just the subcohort member at risk, and 2 the Prentice method where risk sets are augmented by nonsubcohort cases when they fail. The asymptotic Self—Prentice method variance—covariance matrix and standard errors are computed using the simplification described in Therneau and Li The syntax of predict following stselpre is as in stcox.

Options nohr specifies that coefficients rather than hazard ratios are to be displayed. By default, Prentice method coefficients are saved. However, their variance is somewhat complicated because of the correlation between risk sets induced by the sampling.

Lin and Ying and independently Barlow proposed the use of the robust variance estimator for the case—cohort design as a simpler alternative to the asymptotically consistent estimator provided by Self and Prentice Recently, Therneau and Li proved that the Self and Prentice variance estimator can be obtained by correcting the standard variance estimate with a matrix derived from a subset of dfbeta residuals.

Both estimates are now available in Stata. In estimating the model, three methods can be implemented: 1 Prentice, 2 Self and Prentice, and 3 Barlow. They differ in the composition of risk sets and in the weight ascribed to the nonsubcohort case and to the subcohort member.

Both aspects can be handled by preparing an appropriate dataset and by using as offset terms, the log-weights stored in the variables created by stcascoh. Example continued In their analysis, Breslow and Day found three significant risk factors. Here are the results in the full cohort:.

We begin with the Prentice method. In this command, standard errors derive from the Self and Prentice model-based variance—covariance matrix. Note that they are similar to those calculated using the robust estimator. If self option is used, coefficient vector of Self and Prentice method are saved.

Let zi t be the covariate vector and Yi t an at risk indicator for individual i at time t. Both segments are retained for subcohort members who fail. In the other two methods, the weights must be specified. In Stata, the weights can be incorporated as an offset term; the logarithm of the weight must be used.

The Self and Prentice method employs in the denominator just the subcohort members. This can be accomplished by setting the offset to zero for all observations in the subcohort, whereas for nonsubcohort cases setting the offset to , a value corresponding to a weight less than 10;40 that ; effectively allows exclusion of this observation from the denominator of the risk set. The Barlow method requires that the offset be zero for all records corresponding to failures.

Note that Therneau and Li use a data setup slightly different than the one described in this section. When dfbeta residuals are at hand, it is straightforward to obtain the subset of the matrix through the usual matrix accum command. References Barlow, W. Robust variance estimation for the case-cohort design.

Biometrics — Barlow, W. Ichikawa, D. Rosner, and S. Analysis of case-cohort designs. Journal of Clinical Epidemiology — Breslow, N. Statistical Methods in Cancer Research, vol. Lyon: International Agency for Research on Cancer. Clayton, D. Statistical Models in Epidemiology. New York: Oxford University Press. Langholz, B. Nested case-control and case-cohort methods of sampling from cohort: A critical comparison. American Journal of Epidemiology — Efficiency of cohort sampling designs: Some surprising results.

Lin, D. Cox regression with incomplete covariate measurements. Journal of the American Statistical Association — Prentice, R. A case-cohort analysis for epidemiologic cohort studies and disease prevention trial. Biometrika 1— Rothman, K. Modern Epidemiology. Self, S. Asymptotic distribution theory and efficiency results for case-cohort studies. Annals of Statistics 64— Therneau, T.

Computing the Cox model for case cohort designs. Lifetime Data Analysis 5: 99— The Hernes model has been widely applied in demographic studies. The author proposes to use the least squares method for model estimation and illustrates the use of the command with U.

Keywords: Hernes model, first marriage, diffusion model. Hernes developed a diffusion model for the process of entry into first marriage to explain the bell-shaped hazard rate of entry into marriage. In this model, he posits that two competing structural processes explain the time dependence in the process of entry into marriage. On one hand, with rising age t, there is an increasing proportion F t of a cohort that has already entered into first marriage, which in turn enhances the pressure to marry on those who are still unmarried.

On the other hand, there is some sort of decreasing social attractiveness and, more importantly, a declining chance s t of contact between unmarried peers with increasing time t. We assume simply that each person starts out with a certain marriage potential, Ai , but that this potential declines with a constant proportion b for each time unit, where b is the same for all individuals.

Thus, over time, marriageability is a geometric progression; it decreases with a constant proportion for each time unit. In practical terms, this means that in an empirical curve fit, we must take as t0 the first year of the process. To estimate the model for a given set of observed cumulative marriage rate F t , we need a technique to estimate parameters F0 , A, and b in formula 5 , or equivalently, k , a, and b in 8 from which F0 and A can be calculated.

Once they are estimated, we can compute the predicted percentage married from the model for increasing values of t and compare these calculated values to the observed ones. Hernes proposed to use a simple procedure developed by Prescott for estimating the parameters of the Gompertz curve from the cumulative observations over time. Since the curve has three parameters, three equations are needed to find them.

The above procedure has the advantage of easy calculation but does not provide the measurement of accuracy of estimated parameters. In addition, it yields the estimated age-specific cumulated marriage rates and age-specific differences between the observed and estimated cumulative marriage rates.

Options method string specifies the method for estimating the Hernes model, either hernes for the Hernes method as described above or nl for the nonlinear least squares method. The default is the nonlinear least squares method. Examples We use the data of the cumulative first marriages for white women born in —24 in the United States from the U.

Bureau of Census to demonstrate the use of hernes to fit the Hernes model. The largest deviations from the least squares procedure are found for ages 26 and 27 at which points the percentages married are overestimated by 0. For the Hernes method, the largest difference is found for age 22 at which point the percentage married is overestimated by 1.

The degree of fit for the least squares method is seen more clearly in Figure 1, which plots the observed cumulative first marriages against age together with the fitted curve. Observed and fitted first marriages versus age using nonlinear least squares. The hernes command can also be applied conditionally using if and in expressions as shown by. References Hernes, G. The Process of entry into first marriage. American Sociological Review — Prescott, R.

Law of growth in forecasting demand. Keywords: regression output. I have fixed some small bugs in outreg, a program described in Gallup , , that writes regression output to a text file. References Gallup, J. Stata Technical Bulletin 28— Stata Technical Bulletin Frechette, Ohio State University, gurst1 econ. This increase in speed stems from the use of analytical first derivatives in the computation of the quasi-newton step.

Keywords: random-effects ordered probit, gllamm6, quasi-Newton algorithm. Introduction Recent developments in computing power have allowed the estimation of increasingly complex problems. One such class of estimators is allowing for individual specific effects when analyzing limited dependent variables. The first example of this in Stata is rfprobit introduced by Sribney This was followed by the inclusion of the random-effects option in xtprobit, and more recently by the creation of gllamm6 by Rabe-Hesketh, et al.

However, the latter relies solely on the computation of the likelihood for the optimization, that is, the first derivatives and the Hessian are numerically approximated, and thus can be very slow, even for relatively simple problems. I propose a program, reoprob, which makes use of the analytical first derivatives and, thus, considerably improves performance.

Options i varname is not optional, it specifies the variable corresponding to an independent unit for example, a subject id. It is optional, and the default is Increasing this value improves accuracy, but also increases computation time. Computation time is roughly proportional to its value.

Use the trace option to view parameter convergence. The ltol and tol options can be used to loosen the convergence criterion respectively 1e-7 and 1e-6 by default during specification searches. As Butler and Moffitt demonstrated, this is amenable to Gaussian quadrature. Of course, this is sufficient to estimate such a model as one can use numerical approximation to the first and second derivatives to compute quasi-Newton steps.

This, however, makes every step fairly long to compute, even for a relatively small sample. This can be improved upon since the first derivatives can also be approximated by Gauss—Hermite quadrature. Examples To demonstrate and test reoprob, I will investigate the effect of income, schooling, and political freedom on the degree of bureaucratic corruption in non-OECD countries.

To this end, I will use data from 87 non-OECD countries over a 16 year period — on the level of bureaucratic corruption produced by the International Country Risk Guide. Not all years are available for every country, however. The corruption index CI ranges from 0 to 6. It is reported on a monthly basis, but I am using annual averages.

Income is taken to be GDP per capita, and education is measured as the ratio of total enrollment in primary school, regardless of age, to the population of the age group that officially corresponds to the primary school level. Estimates are based on the International Standard Classification of Education. Political freedom PF is given by the Gastil index of political rights. The Gastil index ranges from 1 to 7, one being the highest degree of political freedom. For the purpose of comparison, however, I will first look at a simplified problem.

The only regressor will be income. This will be estimated using 12 points for the quadrature. Estimating the complete model yields similar results. Regressing CI on income, education, and PF, it takes 13 minutes and 14 seconds for reoprob to converge versus 44 minutes 35 seconds for gllamm6; again more than three times slower.

This, however, should not be expected to be true in general. There may well be problems for which the opposite is true, it is simply a question of the stopping criterion being affected by the differences in the analytical and numerical gradients. These results are presented in the table of determinants of corruption in non-OECD countries given below. Stata Technical Bulletin 27 Hence, this paper has shown that reoprob computes the likelihood for a random-effects probit correctly.

Furthermore, it has provided examples of the considerable increase in speed that may be achieved. References Butler, J. A computationally efficient quadrature procedure for the one-factor multinomial probit model. Econometrica — Greene, W. Econometric Analysis. Rabe-Hesketh, S. Pickles, and C. Stata Technical Bulletin 47— Sribney, W. Stata Technical Bulletin 15— These include means normal distribution , proportions binomial , and expected frequencies poisson. Brief review of correlation confidence intervals I will give a reminder of the algebra of correlations, following Altman The new commands ci2 and cii2 behave exactly as ci and cii, except for the extra options corr and spearman.

Without them, these formats are invalid. Examples We begin with cii2 operating as cii, and as for correlations. Saved results Whichever command is used for correlations, the following are saved in r : r n number of observations r r correlation r lb lower bound r ub upper bound r corr ci2 only correlation type Otherwise, results are saved as for ci and cii. Reference Altman D. Relationship between two continuous variables.

In Practical Statistics for Medical Research, ed. Altman, — London: Chapman and Hall. Keywords: life table analysis, vital statistics, causes of death, survival analysis. The life table is one of the fundamental tools of vital statistics analysis, either when used from an epidemiological standpoint or from the perspective of actuarial science. As we know it today, the method was formally established in the transition of the 17th to the 18th century by Edmund Halley and John Graunt , and afterwards became a focus of attention to many other distinguished men of science, such as Benjamin Gompertz , in the first quarter of the 19th century.

Although interest in mortality records can be traced back to the 3rd century Roman Empire mortality registries, the systematic compilation and publication of mortality statistics only began by the end of the 19th century. For instance, the first American official life table ever published came to light in Selvin Life table construction and analysis provides an alternative to standardization as an appropriate method to describe the pattern of the survival experience of a large population or of one of its subgroups, given only that we possess a set of age-specific mortality rates, or more elementary data allowing their computation, such as number of deaths, and midyear population estimates for each age strata Armitage and Berry ; Chiang Some developments of this approach are also useful to evaluate the impact of competing risks as they act upon a group, as well as to obtain data to draw survival curves, survival probabilities, and hazard functions Selvin Generally, a distinction is made between cohort or generation life tables and current life tables.

While the former variant aims at describing the actual observed survival experience of a group or cohort of individuals born at about the same time a generation cohort followed up through time, the latter type describes the survival pattern of a population group subject throughout life to the age-specific death rates currently observed in a particular community, as though no significant cohort effects, for example, generation variability influences exert their actions.

Both these two life table forms are quite useful in the context of epidemiological or vital statistics studies. While the current life table technique provides an alternative method to standardization when comparing the mortality experience or the burden of disease of different groups, the generation life table approach is particularly useful in the context of occupational health studies; namely, to investigate the patterns of observed mortality in specific professional groups followed up over a long period of time Armitage and Berry Another commonly-made distinction separates abridged from complete life tables.

Being an approximation, its use is mainly justified by computational constraints, or by lack or scarcity of the data. On the other hand, a complete life table may also be aggregated into 5- or year age groups Anderson Chiang , as well as others for example, Armitage and Berry ; Anderson emphasize that the technique of construction of life tables, such as those published by life assurance offices or national sources of vital statistics, is a rather complex one. However, Hill and Hill , as well as Selvin describe quite simple construction strategies which, being simplified and accessible to almost anyone, may prove quite useful either for pedagogic purposes, for epidemiological research, or for surveillance.

According to this approach, a population life table, as well as several derived e e statistics, such as the at-birth, 0 , and age-specific, j , expectation of life estimates or the corresponding survival probabilities or hazard rates and functions , can be generated if we dispose of a set of observed age-specific mortality rates or data allowing their computation, such as the number of recorded deaths and number of persons at risk for each age interval.

The command options provided allow not only the computation of general life tables for all causes of death at once, that is, single-cause life tables , according to desired if or in clauses, but also for specific population strata, for example, sex groups discriminated by means of a by option. In addition to the tables just mentioned, lifetabl also allows the analysis of the impact of multiple specific causes of death option sclist on the pattern of human mortality.

Up to 20 different variables registering the number of deaths related to particular causes in each age strata may be added through the sc option. Moreover, if requested by the option allsct, the program will also display tables for observed number of deaths by each cause and age level Dxi x dxi , for the life table expected number of deaths, by each cause at each age level , and, finally, for the life table expected total number of deaths by each cause occurring after each age x Wxi.

Throughout the program output, the notation used for the labeling of life table columns, as well as indicators such as those just described letters and expressions between parenthesis above , strictly follows the conventions adopted by Selvin On the other hand, the output labeling for statistics related with the potential years of life lost group of indicators derives from the suggestions of Murray and Lopez See the Methods and formulas section below for further details on the procedures and definitions.

With the lifetabl command, it is also possible to produce five different groups of graphics. Options ge, gp, gs, gh, and gsc allow users to request the graphs of, respectively, expectation of life function s , cumulative distribution s of expected deaths, survival function s , hazard rate function s , as well as other graphics related to the specific causes of death included in the command.

Option grphs requests all five graphics at once. Since the program has several options to control the extent and type of outputs for example, not, noo, noyll, allsct and can produce very long series of tables or a large number of graphics, particularly when the by or grphs options are used together, we strongly recommend the user to begin by exploring the program with one of the example databases included with this insert.

Minimal specification In order to produce a life table with the lifetabl routine, it is necessary to specify at least 1. Through the command option strata a numeric or string variable, coded in such a way as to adequately describe the different age strata for example 1, 2, 3, A variable containing observed strata specific mortality rates option rates 2b.

Two variables coded with, respectively, the number of death events registered for each age during the time interval considered option deaths , and the number of persons in the same age levels usually the mid-period population estimates; option pop. Regarding the strata option, the values used to designate the successive age intervals must be unique within if or in subgroups and must also keep the natural order of the successive levels when sorted by the program.

For example, a string variable coded "[[", "[[", "[[", When in doubt, perhaps a safer alternative is provided by the use of a naturally ordered numeric variable to designate the successive strata in this option, together with a string variable, which may be declared through option label to provide labels for the output.

This alternative instructs the program to use as labels in the output the first seven characters of the strings contained in labelvar. Stata Technical Bulletin 31 If the program is run through the specification of observed rates rates ratesvar , these must be constructed in order to represent number of events for 1, 10, , 1,, 10,, ,, or 1,, persons. If the rates multiplier is other than , the default value , the exact value to which the recorded rates are referred to must be explicitly declared through the option multip.

Use of this last option is allowed only when option rates ratesvar is also utilized. However, regardless of the power of ten of the rates used, the figures shown in the life table column Rx for the life-table age-specific mortality rates are always referred to number of events per , individuals.

Although the radix is an essential element from which all the life table is derived, this option rarely will need to be used, since the default will be adequate for the majority of circumstances. Another important technical detail of the life table construction regards the evaluation of the contribution made to the total time lived by a cohort who entered any age interval l0 ; l1 ; : : : ; lx by those who die in that same period d0 ; d1 ; : : : ; dx.

Generally, it is assumed that, on average, those who die during each age period were alive for a time of approximately half of the total interval length. However, for life tables in which the interval lengths considered are equal to one year for ages following birth complete life tables , that approximation is not valid. Indeed, during the first few years of life, deaths tend to occur not symmetrically around the midpoint of the interval, thus originating an overestimation of the same interval life table stationary population Lx.

Usually this problem is dealt with by some form of correction made to the general rule above. One of the methods available, reported, and adopted by Selvin is the specification of weights other than 0. The lifetabl option weights allows the specification of such weights.

If the option is ignored and the interval lengths of the life table intervals are all of one year, the weights automatically used by the program will be those empirically determined by Chiang and reported by Selvin for, respectively, the first four years of life: 0. At all subsequent intervals and in all circumstances, the contribution of each death to total time lived in the age segment is considered to be equivalent to one half the period length that is, 0.

On the other hand, if any of the life table age intervals extends itself for more than one year, the program automatically makes this parameter equal to 0. One other option, nyears numvar , allows the user to inform the program about the name of the numeric variable which registers, in years, the length of each age interval. If this option is not used, the program assumes that all age periods are of one year length.

Unless one of the two options just mentioned is included in the command line, the original data will always be restored or reconstructed at the end of the processing, thus protecting any user variables with names similar to the ones listed below in the original file. Kept variable names and their content are the following: Rx life table mortality rates per , persons , qx probability of dying in the x age interval , dx expected number of deaths in the age interval , px probability of surviving the age interval , lx number of people alive at the beginning of the age interval , Lx cumulative years lived through age x , Tx total time lived beyond age x , ExpYL expected years of life at age x , Surv survival probability , SurvVar Greenwood variance for Surv , and Hrate hazard rate.

If specific causes of death are also being considered in the analysis requested at the command line, three other sets of variables, respectively suffixed 1, 2, With some of these st commands, it is also possible to produce several variants of the classic life table here presented, provided the original data are recorded at the individual level single observations followed-up through fixed or variable length time intervals.

However, with the available st commands, it is not possible to produce life tables for whole populations based on vital statistics data aggregated at the level of age groups as shown in the examples provided below. Options strata age level var allows the specification of a numeric or string variable coding the different age strata. This option must always be specified. If the variable used is numeric, the values representing the successive age strata must be monotonically ascending numbers, because during processing, this variable will be subject to an ascending sort, and the concrete values recorded will be used as labels for the strata for example, 0, 1, 2, If the alternative possibility of specifying a string variable is utilized, the same also applies.

A perhaps safer alternative is the use of a numeric variable with ascending integers to designate the successive age levels in this option together with a string variable to provide labels for the different age strata in the output through option label. In every circumstance, the within if, in, or by subgroups variable describing the age strata cannot have repeated, neither missing nor null, values. Use of this option is mandatory, unless the following two options are used instead.

The age-specific rates can be expressed in terms of several population multipliers powers of ten. However, if the specific power of 10 for which the rates are referred is not , the default , its value must be specified through the option multiplier. This option must always be used in conjunction with the previous one whenever option rates is not available nor specified simultaneously. When this option is not used, it is assumed that all age intervals are equal to one year in other words, it is assumed by the program that the life table being calculated is a complete life table.

The within subgroup value for the last interval an open one is always re set to one. The default value, assumed whenever this option is not used, is again These will include estimates for the 1 at birth, and lifetime beyond age x conditional probabilities of death for each specific cause Pr death by cause ijage x , 2 absolute risk of dying by each cause, given a certain age, during the following interval qxi , 3 cumulative distributions of deaths by cause and age Fxi , and 4 probabilities of death after a certain age x, given that the death is caused by each of the specific categories considered.

Whenever this option is utilized, it is safer and wiser to also use option deaths deathsvar to explicitly declare the total number of deaths observed to occur in each age strata. However, this requirement is not absolute because, in the absence of an explicit declaration of the total number of deaths in each age level by all causes , the program automatically assumes that the row sum of the variables included in option sclist varlist equals the just-mentioned total.

Of course, if that is not the case, the results may be compromised. So, when the deaths deathsvar option is not being used, care must be taken to assure that this assumption holds, for instance by including in the sclist varlist option, one variable for a residual specific cause-of-death category corresponding to the remaining, not otherwise explicitly considered, causes of death. It is only necessary that these rates are all referred to the same number of persons power of ten as the ones eventually included in the option rates ratesvar , and that another option, allrx signifying all specific causes are in rates is also used to inform the program of this particular circumstance.

If neither of these is available that is, if strictly only rates are declared , the program will not be able to calculate the potential years of life lost indicators. The quantities specified must be expressed in terms of the proportion of the total interval presumably lived by any person ultimately deceased anytime during the same interval.

The weights option allows the modification of the default values for one, or all, of the first four periods of living. By default, the weights used by lifetabl are those used by Selvin which, apparently, were taken from Chiang In fact, they are equivalent to an explicit specification of this option as weights 0. The variable number of parameters passed to the program is interpreted according to their order, as pertaining respectively to the first, second, third, and fourth age intervals.

Concerning all the time periods following the fourth, it is also always assumed that each death contributes to the total time lived in each age level by the cohort of people alive at its beginning with a time equal to one half of the respective interval length. The default value used by lifetabl is pyll 65 , following the convention adopted by the U.

Centers for Disease Control and Prevention, and also by a number of other national and international agencies. In this option, as well as in all outputs of the program, we also complied with the Murray and Lopez suggestion of always explicitly indicating the upper age limit used in the calculations. By default, lifetabl restores the original dataset after processing. However, when option keep is included, the user data is left behind, unchanged, and a new datafile, with an added set of variables, but truncated according to any if or in expressions also utilized in the command, is kept in memory.

By default, this new working file is saved under the name SaVeD. The variables added to the original set are Rx Life table mortality rates, per persons qx Probability of dying in interval dx Expected number of deaths in interval px Probability of surviving the interval lx Number of people alive at the beginning of the interval Lx Cumulative years lived through x Tx Total time lived beyond x ExpYL Expected years of life at age x Surv Survival probability SurvVar Greenwood variance for Surv HRate Hazard rate label labelvar specifies a string variable to be used in the outputs in the substitution of conventional ordered values in the naming of the successive age levels.

In contrast with the truly optional use of this label option, the user is always obliged to also specify one variable which may be the same through option strata age level var , in order to clearly indicate the correct ordering of the age levels. Due to the output space available, the strings stored in labelvar will appear truncated in the output if they are longer than 7 characters.

Allowed values are powers 0 through 6 of ten. The default value for the rates multiplier, assumed whenever this option is not used, is Following this option, only graphs will be displayed provided they have been requested in the same command line. These supplementary tables exhibit the observed number of deaths by each cause and age D x d level xi , the life table expected number of deaths by each cause at each age level xi , and the life table expected x W total number of deaths by each cause occurring after each age xi.

The name for the file must be fewer than eight characters, according to the general naming rules. This option may be combined with replace to allow the program to substitute any existing file with the same name. The same graphs may instead be produced individually by using the next five options.

Examples The examples provided below use three different data files allowing a complete exploration of the lifetabl command. The first dataset, named lifetabl. The second file, mcauses. This file also includes variables registering the number of observed deaths in each year-sex-age-strata due to some specific causes of death.

The third data file included in this insert, 4deaths. It was also prepared with data taken from Selvin , with the purpose of allowing a cross-validation of the lifetabl command outputs by replicating the numeric results published by that author. Source: Selvin, Source: Selvin, vars: 11 19 Sep size: 7, Suppose we want to produce a complete life table for the male population.

Notice because we have redundant data in our dataset observed rates together with number of observed deaths plus population, for each strata , that exactly the same output could have been produced by. The last example also illustrates the use of observed age-specific mortality rates referred to a number of people other than the , default value.

Because we have never specified a variable to label the successive age intervals, the age strata were labeled as 1, 2, 3, Notice further that we could also have requested 9. Until now, it was not necessary to use the option nyears age interval length var due to the fact that we have been dealing with complete life tables. Automatically, the program assumes these conditions hold whenever not finding an explicit nyears age interval length var option modifying the default assumption.

Let us also consider the request of one or more of the available graphs. It is only necessary to add, to any variation of the commands considered so far, the respective option s. For example, the command. Expectation of life function for lifetabl data.

Figure 2. Cause of death density for lifetabl data. Cumulative distribution of expected deaths for lifetabl data. Figure 4. Survival functions for lifetabl data. Hazard rate functions for lifetabl data. Example 2 Next, we illustrate the use of lifetabl in the context of the analysis of multiple causes of death. We use the mcauses dataset. Source: INE, vars: 13 20 Sep size: 6, However, the data stored in this file is a bit more complex than the data of the lifetabl. One other feature of this dataset is that the age intervals are bigger than one year in length.

In fact, data within each year-sex group is available only for since birth, successive five year intervals. Thus, we are not dealing with the standard conditions required for the computation of a complete life table. However, since we do possess one variable codifying the length of each age strata nyears , it is still possible to approximately estimate the life table s , provided that we use option nyears varname to instruct the program that we are dealing with nonequal or nonequal-to-one year age lags.

For instance, if we were again simply interested in the calculation of male and female life tables for the calendar year , we would use. So if the null hypothesis is a straw man, why bother testing it? After all, you already know it's false.

What you really want to know is something more like "is the difference large enough to matter? So now you have an estimate of the group difference along with a sense of how precise that estimate is. If all of the values contained in the confidence interval are big enough to matter for practical purposes, then you can confidently assert that there is a meaningful group difference.

If none of them are large enough to matter, then you can confidently assert that the difference between the groups is too small to matter. If the confidence interval spans differences that include both large enough to matter and too small to matter, then your conclusion must be tentative: my best estimate matters or doesn't, as the case may be , but the data are compatible with the opposite being true.

The p-value gives you none of that; it just tells you whether something you already know to be false is incompatible with your data. Carlo Lazzaro. I guess I see your point but my output implies that I should accept the null hypothesis that the difference of the coefficients are zero. So should I still worry about the confidence intervals when P is large? You cannot accept the null hypothesis unless you have first done a formal a priori power analysis showing that you have adequate data to support that conclusion.

Without that, you can only reject the null hypothesis if p is sufficiently small or fail to reject the null which is not the same as accepting the null--it is more like being agnostic about it. So, your output does not , by itself imply that you must accept the null hypothesis.

By itself, it just says you can't be confident the null hypothesis is false--but that doesn't even come close, by itself, to making it true. And really, ask your self, if you had no data available, would you consider it at all reasonable that there might be no difference whatsoever between the two groups?

If so, then testing that null hypothesis takes on a small bit of reasonableness. But if not the more usable case , then testing the null hypothesis, though often done in practice because people don't think about it, makes no real sense--what you would really want to know is whether the difference matters. That leads you back to my line of reasoning in 4. Thank you very much for the explanation. Given my results, 1 I fail to reject the null which implies that the difference of the coefficients can be small Nazlika: Code:.

A is a valid model incorrectly interpreted. To see if the effect of lfx differs between high and low import you have to look at the coefficient of group lfx, not at the coefficient of lfx. B is probably an invalid model. Dummy is constant within ID. I guess I had a mistake in the previous model as I have interacted all the independent variables.

In this version, I got the same results from both models. I have one another question. For another specification, I run a difference GMM regression instead on xtreg. I divide the sample into three categories based on firm characteristics which are constant over ids.

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